Have you ever been judging at a piano event and when you tell the student that they can take a minute to warm-up before playing they tentatively depress the notes of a C-major chord and then quickly assure you that they are ready? I’ve had this happen on more than one occasion. Sadly, I’m sure that my own students have done this on more than one occasion, too!
One aspect of preparing a student to play well in an audition, evaluation, or competition is equipping them with helpful ideas for warming up at the piano on which they are to perform. Albert Frantz, of the Key-notes Piano Blog, has some good suggestions in his post, Warming up for Lessons and Performing, that I would recommend reading over so that you can pass them on to your students.