Video interviews add their own anxiety: the frozen screen, the fear of talking over someone, seeing your own face.
Remove the mechanical worries
Test the link, the mic and the light an hour ahead. Most pre-interview panic is really uncertainty about whether the technology will work.
Hide your self-view
Watching yourself is uniquely distracting. Most tools let you hide it. Do that, and your delivery relaxes noticeably.
Warm up your voice
Say your first answer out loud once before joining. The first thirty seconds of any interview are the shakiest, and having already said the words takes most of that away.
Common questions
How do I stop my voice shaking?
Speak your opening answer aloud before joining, and slow down. Slower speech steadies the voice.
Is it okay to admit I am nervous?
One brief acknowledgement is fine and often relaxes both sides. Do not return to it.