I suppose if you use an electronic metronome, you can put it in silent mode? The lights will show you the beat, but no clicking sound may allow gradually getting back in sync without rushing?
On tempo and rushing
ShiroKuro BTW when playing the entire piece w metronome, what do you do when you have a fermata, rit, or other tempo variations? How do you get back in sync the metronome without unnatural pauses?
When I play with metronome I don't make tempo variations. For a fermata I hold it an even number of beats.
ShiroKuro BTW when playing the entire piece w metronome, what do you do when you have a fermata, rit, or other tempo variations? How do you get back in sync the metronome without unnatural pauses?
I ignore the metronome during the tempo variations and find it usually quite easy to stretch the fermata or rit to fit in with the metronome, so I can start the new phrase together with the metronome again.
It is harder with longer tempo variations. Finding a YT recording of someone playing these tempo variations really well and alternating between playing together with them and playing alone helps a lot.
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... feeling like the pianist on the Titanic ...
The thing about metronomes is that they're supposed to be a teaching tool to get us to count internally. If you have to rely on a metronome to keep steady then you don't have an internal sense of timing.
WWII soldiers and POW's learned to count seconds in their heads and got extremely accurate at it because they practiced it until it was second nature. That's what all the basic beginner clapping and tapping exercises were designed to do - teach you internal timing.
Regarding rit and other tempo variations; if your metronome is silent or you don't use a bell to indicate the first beat, then it doesn't matter which "tick" you use to pick up for the beat. It's just timing and 1,2,3,4 is exactly the same tempo as 3,4,1,2.
Player1 If you have to rely on a metronome to keep steady then you don't have an internal sense of timing.
This comment may have been meant as a general comment and may not have been directed at me, but I am defensive enough I feel the need to say that, in general, I have a very good internal sense of timing.
But obviously, control of tempo variations — not just control of tempo — is an aspect of musicality, along with dynamics, that is an area with endless possibility for improvement and polishing.
ShiroKuro I am with you on this one. Rhythm is an area I have the least amount of difficulty with. Yet I too notice a tendency to slowly speed up as a piece is played through, especially when I purposely start slower for practice.
When I think more about this problem, I wonder if this is similar to relative pitch vs absolute pitch. Keeping perfect rhythm in a phrase and through several phrases is like relative pitch. But keeping a steady and specific beat (at what exact tempo desired/chosen) for a long time, or come back to that tempo from rubato/fermata, is more like absolute pitch, and therefore harder. Also I feel overall memory of aural impression of piece also influence this because for pieces that I know well it’s even harder to play it at different tempo.
I wasn't trying to point a finger at anyone. All I was saying is that, in general, if you have to rely on an external device to keep time, you need to work on your internal time sense.
Here's an observation; clocks have been around a long time but music has been around longer. Without a machine to keep time, how would musicians learn and keep tempo? It's an internal thing, not an external one.
ShiroKuro And what we concluded was that I may be sort of rushing to cover up the mistake, or replace it with correct notes, or rush to the next passage.
I had a bit of a "self examination" about this very topic not all that long ago. I usually play with a drummer so they normally try to keep a pretty steady beat going. There are times when any in the group start "rushing", not sure of all of the reasons. But I did get to thinking about me and why I do it when I do it.
There were several things I observed about myself. I think the #1 thing I did that turned into "rushing" was actually an uncertainty about the next note and "feeling for it" a bit ahead of time. And by the time I'd assured myself I'd found it, I'd played it, usually just a tad too soon. Add a few of those up and it's "speeding up the tempo". That tends to resolve itself as I become more comfortable with a piece and don't do as much guessing.
A second thing I sometimes catch myself doing is "speeding up" parts of a song for rehearsal purposes, usually parts I am very familiar with and really don't need the practice so much as I need to lead in to a section of the song that I do need practice on. I can get accustomed to playing it too fast and then if I'm not careful, I can get on stage and start out playing much too fast, mostly out of habit. It may not be an issue for many who don't have a long song list. There are times when we have extended gigs where there is up to about 5 hours of music, zero repeats. Just to play through every song one time, as it would be performed, no go-backs / repeats, takes a full 5 hours. That's a lot of time. So rushing through or even eliminating parts that just repeat, second / third verses, stuff like that, saves time and allows for some targeting of the more important things... intros, endings, solos, and just remembering the correct A section going with the correct B section, etc. And I do not play with music on stage. It's is ALL in my head. My music stand has a song list... name of song, key, and if there is anything peculiar, a few words to nudge my memory. (Probably TMI.)
I'm sure there are lots of other things that others have, individual quirks. Those are just two of mine. But it was an interesting thought process to try to pick out WHY I was speeding up when I shouldn't.
Of course, sometimes we just get excited and wanna go faster! 
ShiroKuro BTW when playing the entire piece w metronome, what do you do when you have a fermata, rit, or other tempo variations? How do you get back in sync the metronome without unnatural pauses?
You can try different strategies, depending on the piece and what aspects you are aiming to practice.
Straight through with no rubato. This can be an interesting experience, especially with a piece that normally has a lot of rubato. A while ago I tried playing through the whole of Chopin's 4th Ballade like this. It was very strange and certainly not recommended for a performance, but it taught me a lot about how much liberty I was taking at different points, and did in fact inspire me to rethink certain tempo variations.
As Anmisha suggested, ignore the metronome during a rubato passage and fit in again when you get back to a strict tempo passage.
Stop the metronome for a ritenuto and start it up again when the piece goes back to tempo. This does chop the piece up somewhat, but is ok if there aren't too many stops.
For those with the necessary programming skills, create a click track with all the rubato programmed in. I've never actually done this (too much hard work!) but I've often conducted or played to click tracks: this can be a very interesting experience.
In all cases, I don't just ignore my own internal pulse. I'm constantly comparing it with the clicks of the metronome, learning which passages feel faster or slower, even though they stay the same speed. Once I've played the piece a few times with the metronome, I'm much more aware of when I change tempo for musical, expressive reasons and where I change tempo without good reason.
iternabe especially when I purposely start slower for practice.
Yes. I find that if I have a general tempo that I usually play the piece, with a piece that I'm well past the learning stage and into the polishing or performing stage, that becomes my "set tempo," in my body, for that piece. So say I want to slow down for some particular purpose, and play it much slower than I normally do, I find that very challenging because my body wants to play it at its usual tempo. This is a kind of muscle memory, IMO.
When I think more about this problem, I wonder if this is similar to relative pitch vs absolute pitch.
Oh yeah, that's super interesting, I've never thought of it that way!
Player1 I wasn't trying to point a finger at anyone.
Thank you. I can sometimes be a little touchy. I still take a lessons, and I always appreciate the ideas I get from online discussions like this one. Which is to say, I still have a lot to learn and lots of room for improvement. But I've been playing piano for 25 years now, so I bristled at the suggestion that I don't have an internal sense of timing...
Re your comment about clocks, interesting comparison.
I don't disagree with your point that timing, tempo, is an internal skill. It has to be felt in order for the pianist to play in a way that's convincing.
But that doesn't mean we shouldn't use the tools available to use. A metronome is just that, a tool, and as such, it has a place in the toolbox of practice strategies.
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I think those two are related, but not necessarily the same thing (timing and tempo). One can have a fantastic sense of tempo and keep the same speed throughout, while their timing is all over the place. Or it is possible to have great timing (all individual notes played completely correctly in length) while speeding up throughout the tune like a wind up toy in reverse.
Especially the latter is very common in amateur bands - they start at (say) 80 bpm and get so enthusiastic in their playing, that they finish the song at 130. Often it doesn't even get noticed by anyone, unless there is a recording and one listens to it again from scratch.
Neither are super easy to correct so I can't offer any advice except to stay alert and try to be aware of it before it happens... yeah. Easier said than done Especially when nerves play nasty tricks on you. The good news is that it's a live performance and there is a huge chance that people won't notice it because they're not there to nitpick, they're there to listen to you perform and root for you all the way
Sophia Neither are super easy to correct
One thing I've been doing is making sure to breathe at the transitions and ease into them... It's hard to explain without reference to a score, but there are natural phrasing points and "breath" points. I find that acting like I'm a singer who needs to take a breath helps with the "nerves induced speed ups" and offers a chance to recalibrate, like if I was speeding up through the last section (say to cover a mistake, as was the original topic here), then making sure to take a breath at the transition helps ... we'll see if that works during the concert, but it worked pretty good in my most recent practice recording.
Nice, I really like that suggestion. I forgot whoever mentioned the holding-breath-as-survival-impulse that we somehow need to overcome, but I agree that this would seem like a great way to go about it. I'm sure you will do fine 
Player1 I wasn't trying to point a finger at anyone. All I was saying is that, in general, if you have to rely on an external device to keep time, you need to work on your internal time sense.
I use the metronome to train my internal time sense. It does a great job of identifying the areas where my internal time sense is off. In other words, if I need to work on my internal time sense, which I frequently do, I use a metronome. 
5 days later
Recently, instead of trying to play to a metronome, I am trying a different method to check my rhythm and beat. I play back my play through, and clap my hands loudly to the beat and keep the clapping steady. It's quite easy to find where I speed up, or rush a certain note this way. Granted I am only playing very short pieces. But being able to detect what's the cause of rush and what to fix seem quite effective for me.
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iternabe Thanks to the link WieWaldi provided a while ago, I find it very helpful to "tap" along instead of just clap. It it is not 100% accurate, but will at least tell you if you finish at the same tempo as you started
Another very efficient way (for me) is by playing simple duets. Record one part and play along with your recording (without metronome). It's harder than it seems and is guaranteed to expose any "shortcomings" you may have in that regard It was quite a humbling experience to me... though I'm getting slightly better at it.