In the beginning I had problem playing pieces away from home even the ones I played perfectly in practice. Part of the problem was practicing on a DP at home and then switch to an acoustic instrument in public. I would play wrong notes since the action feels unfamiliar. Once I tried to play a movement of Bach French Suite 3 on an upright at a friend's house but stumbled all over.
I have access to a piano at the conservatory where my lessons are held so switching between a DP isn't a problem. Besides playing your pieces perfectly, you need to be able to start your pieces at various places so when you start to play wrong notes, you can pick up from the next section. As always start with slow practice and be aware of the notes you play than relying on musicle memory alone to solidify your playing.
Once I played an arrangement of a Bach Sinfonia on a Baldwin grand in a piano store. It's a piece compiled from an orchestral score with 6 instrument parts. It's a piece I enjoy listening to so I was listening to it as I play and let my fingers do the work. I was more concerned with the price tag over $10k. If I made a scratch anywhere I wouldn't be able to pay for the damage. It's a piece at a relatively slow tempo I worked on for 3 weeks.
The last piece I played at a friend's house was the first 3 verses of Simon & Garfunkel "Sound of Silence". Besides slight variations between verses, the 5 verses are repetitive. Once I got through v1, I played through the other verses with little stress. Playing a Pop song that is repetitive than a Classical piece with many intricate parts is much easier.