Funny you mention sleep, made. I have a Dickens of a time staying awake on a plane. Even a one-hour flight makes me drowsy for some reason.
My wife is just the opposite, and this is why I say we have to be careful in judging what people go through. She is a high anxiety flyer, too. She couldn't sleep on a plane if her life depended on it. I asked her how she gets through it and she said she practices -- believe it or not -- breathing exercises she learned when she was pregnant.
Once she calms things down to a decent level she will try to read or listen to music or something to keep herself occupied.