I feel you! Most of my favorite skaters are headcases so I've needed to figure this out too.

I stay calm by:
A. Eating
B. Doing stretches/calisthenics/any kind of physical activity while watching (Focusing on doing something hard takes your mind off the skating a little)
C. Similarly, if I don't want to exercise, I like to do things with my hands-I get very fidgety when I watch anything while just sitting there. That's more to just stop myself from getting bored, but usually not a problem during live competition because I don't know what's going to happen so I'm giving it my full attention.
D. Reminding myself that it's just skating, even if it seems like a really huge deal at the time, and no one is going to die if so-and-so doesn't skate well (even if it feels like I will!)
E. It doesn't actually do anything, but it can make you feel better if you have some kind of superstition or ritual that you do for luck. For example, I always wear my favorite color when I'm worried about the outcome of a competition because it feels "lucky." And sometimes I'll do an exercise with as many reps as the PB of the skater I'm worried about (for example, I would do 73 lunge walks if I was worried about Gracie's SP because that is her SP PB). This can be anything from eating the same breakfast before every event to wearing a particular piece of clothing, and although it has no effect whatsoever on the outcome of the event, it can calm you down a little: it's like saying to yourself, "I did what I could-now it's up the the skaters."
Then again, I'm kinda weird that way. But (as a commercial once said

) it's only weird if it doesn't work.