Encourage them to focus on the "big picture." Students can be so hard on themselves if they play one wrong note, yet totally forget to pay attention to the overall musicality of the piece. Tell them to focus on the overall story or emotion that the piece is trying to convey, and that a wrong note is no reason to panic. Just keep going, playing as expressively as possible.
Also, encourage the student to perform their pieces for neighbors or relatives, a small audience of one or two people, or even tape record themselves, just to put a little pressure on as they practice. This will reveal any weak spots.