Make sure you know the pieces inside out, that way you become more confident knowing you aren't going to mess up. On every single one of my exams my hands have been a trembling mess. But I never hit a wrong note because I know the pieces inside out.
Would you mind saying, what did it take you to get to that stage, and how do you know when you have got there? Is it just lots and lots of practice, or is there anything else involved?
I ask because even with a piece I feel I know well, if I'm playing on a different piano, or if it's the first time through when I'm practicing at home, I will make mistakes or not be totally even or whatever, and I don't even feel nervous, I just feel it takes me a couple of attempts before I feel I'm ready. How do you get to the stage of knowing you can do a pretty good performance (even if it isn't perfect because what ever is?) whenever you need to? And how do you know?