Last night, watching TV, I did some thigh stuff. I used a band to pull my thighs apart and a cushion to press them together a la Suzanne Sommers But this morning I had groin pain, almost crampy, actually quite like menstrual cramps.
Did I do something unwise or did I just find some muscles I've never exercised before?

Susan, I am by no means a doctor or other kind of expert, but I would guess that you just used some muscles you're not used to exercising. I know that when I do Pilates and similar stuff, the day after I often feel similar crampy sort of aches. If it fades pretty quickly I bet that's it.