A couple of things come to mind: When you're nervous about doing a song or tune, pause for just a moment before you launch into it and really mentally focus on "locking on" to the proper tempo. I find most of my screw-ups have come from rushing into a piece, and, rushing the beat. Of course, if you start too slow, you can always speed up during the performance :) !

I also think that while you can practice at home until you think a piece is perfect, it's never going to sound the same twice in public. All you can do is get comfortable with it -- and then listen for, and enjoy, the odd little twists and turns the Gods of Sound have decided to lay out for you that day.