All clients receive regular BP testing as part of their tri-annual fitness evaluations. High BP and BP irregularities can be indicative of serious issues and should be evaluated by a medical professional no matter how badly you want to engage a client while they are still excited.
I’ve known a 38yr old who died of aneurysm and a 28yr old who died of minor heart defect during exercise – both tragedies could have been potentially avoided with regular basal health checks including BP.
In addition, be sure to ask if a client is taking medication for high blood pressure or hypertension as these medications will likely show low BP and heart rate even during exertion.
I too use a basic Omron automatic BP machine. Although I find the traditional BP cuff and stethoscope method more accurate, auditory cues can be hard to hear in a noisy gym.