"Nice save at the end, and you seemed so calm." Even if she wasn't, I'd say it so she can start to imagine being calm at difficult moments.
Maybe I didn't express my idea perfectly by adding "even if she wasn't calm." Obviously she wasn't completely calm, but also obviously, she did maintain a respectable level of poise, which I thought could be pointed out to her. She didn't cry, as many children do in that situation, or run offstage without finishing, another popular solution. She stayed in place, kept trying, and eventually finished the piece pretty well, and went on to play a second piece. Another reason to make such a comment to a student, which perhaps I also failed to explain well, is to help her build a vision of herself as competent and calm in a crisis. People live up to the expectations of those they respect, and if she thinks her beloved teacher sees her as calm and capable, she will become even more so.
Thanks, Torp and whynot, for your very helpful thoughts...giving me some hope that I will handle this well!
Practicing in front of strangers has to be done as many times as possible, the more you do it right in front of a handful, the more chance you have of doing it right in a room full of them. So long you pick out what could have been better (there is always something to pick out of in every peformance, nothing is perfect) and you target this, eventually nothing will stand in your way. You need the initial experience that the pressure of a public peformance gives to develop your ability to peform the piece. This first step is always a risk, taking that leap of faith, jumping in the deep end, testing the integrity of what you have been studying. Everyone has failures in peformances it is what makes some people petrified to ever go back on stage. But you shouldn't stop after doing it once, do it again and again, there is nothing lost by doing it only something to gain. Do people remember your errors? Do they think about it the following day constantly? Do they make it their life purpose to remember that someone stuffed up on a piano? Not really, its not that important if you think about it.
Thanks again for all the advice. It was really useful. I asked her today how she felt about the recital, and she said "disappointed," so I told her how proud I was that she hadn't given up and that she had played her second piece so well. We also talked about a lot of things from the forum: practising "performing" as well as "playing" -- this was a big one for her, as normally she doesn't even like her family to hear her (I didn't know this). Also I told her about various musical screw-ups from my life, and how she was probably braver than most of the people in the audience to get up in front of them, etc. I think it did encourage her. Her dad had a very good attitude, too, basically told her it was no big deal. She played the piece really well at her lesson today, so we both know she can do it!