This is my anxiety. I'll just put that out there in the intranets. I'm afraid of failing. Whenever I go to play a piece publicly I am afraid of forgetting the piece, of loosing my spot, of playing it poorly, of stumbling so much that I can't recover- in short of failing.
Here are some great ideas for dealing with that fear of failure
the day of the concert offer quiet distractions like drawing or reading
have your student play the piece for family and friends - reinforce what they did well
talk to your student about what will happen if they make an error - reinforce that it's about recovery and not perfection
remind students that there is no perfect performance - only perfect for THEM
So on the day of a concert I don't practice my piece. I ignore it. I distract myself with a million other things. I practice my technical exercises before I go to play but only to warm my fingers up. When I'm sitting waiting for my turn I try to think of anything BUT my performance because I tend to work myself up. ( Luckily for me a lot of my performances are at concerts I am MC'ing so I get to keep my mind off of my piece. ) After the performance I try to remind myself what I did well and focus on that, only going through the parts that were not excellent to try to learn from them. This is my performance process. It works for me. What do you do when you have to perform?