I take BP readings for someone who gets anxious about them too.
The system we've arrived at is that I play music that relaxes them during the readings. They don't look at the numbers. The first one will be high, so I usually ignore it. I take several readings, look for a couple of consistent ones, then discard any outliers.
Trying to relax always makes me more anxious since it reinforces the idea that there's a danger to be avoided. Over time I've learned the techniques of ERP, which basically does the opposite.
