There is some debate about how much we download our own fears and anxieties onto our children (or our students for that matter). Sometimes it's worth asking WHY a student is anxious instead of assuming (we've all done this, me included).
So here are some questions to ask students about performance anxiety (assuming your student IS anxious)
How do you feel when we talk about playing at the recital?
How do you feel when you play a recital?
How would you feel if I recorded you playing when you are practicing? (why or why not)
Would you like to play your piece for our family? (Why or why not)
Sometimes saying to a student "don't feel nervous" or the like, can cause MORE anxiety or create anxiety where there is none. Instead probe your student to tell them in their own words, with their own experiences, how it feels to perform. Remind them of the amazing amount of work they have put into their piece and how proud of them you are (don't qualify why you are proud of them though!). We are proud of all of our students for having the courage to play their recitals and it doesn't change how proud we are of them if they play flawlessly (no such thing!) or make serious errors. They did it and that's what counts.
Let us know if there are any tricks you've used to deal with anxiety!