Practicing a ton can reduce anxiety, since you'll have confidence that you can most likely solve the problem. Plus, if you practice enough, you'll see so many problems that you might get the exact same problems in the interview. If you do something everyday, it becomes less of a big deal.

Doing other activities that induce this sort of anxiety can help too. I've been a combat athlete my whole life, and the anxiety you get before a match is like no other. Not being able to sleep the night before is the norm, and I've seen people vomit before matches. Plus, it's not a few engineers watching you, but rather a whole crowd of people watching you, with half of them cheering for you to lose. After this experience, live coding interviews are a cake-walk. I get nervous as well with a pounding heart and nervous sweats, etc. But I tell myself I've been here before, and perform as best as I can in spite of it, like I've done before. I generally don't perform quite as well in the interview or match as I do when no one's watching, but that's just how it goes. Learning to perform under pressure like that is a skill that needs to be cultivated.