You try to help them relax, but you don't have much time, and the whole thing is just so unnatural.
Other places I've since been at, and interviewed with, give you a laptop, a problem to solve, and some time. You can focus on the problem instead of the situation much better, and I think that really helps. As an interviewer, it also helps keep some distance from the interviewer. It's too easy to try to micromanage the interview and keep the candidate uneasy. But there's a natural "don't interrupt someone when working" instinct that keeps interviewers more distant when the candidate's programming.
Coderpads on video conference, I think, are pretty good when the candidate has a good space to work in. They're in comfortable territory and you can see them by their keystrokes. The interviewer feels like they're getting more accurate data about how the candidate really operates. I just wish it could do keyboard shortcuts better -- emacs users like me hate seeing Ctrl-N bring up a new window.
The issue of IDE/compiler/keyboard/keybindings is also there, but that's easier to work with.