I will sometimes use breathing when in a stressful situation but I don't use the premie mantra. I either use numbers or a word or phrase. The situation has to be one that can't be escaped and in that case, I have usually taken a Valium already.
One fairly recent example of this was a series of different medical tests, CT scan, PET scan, MRI scan etc. Stuck in a tube for nearly an hour each time while contrast flows through the veins - freaky stuff to me.
Oh yeah, and sometimes when at the dentist I need a little help. Breathing doesn't always relax me - that's what the Valium is for. The best trick is to keep the mind busy while the stressful situation is going on. Doing the times tables in my head is a really good one for that! Thinking complex thoughts takes my focus off the discomfort.