I flew to Italy to propose. Just to be safe, I had a waist pouch for money, passport, and I tied in a little piece of string to tie in the ring. She never suspected a thing. If I just had it in my pocket, I really probably would have dropped it when fumbling for keys, my wallet, etc. The ring didn't set off the metal detector. They are calibrated so that little bits of metal don't set them off. Otherwise anyone with jewelery or zippers or belts or metal buttons would set it off. Think thousands of false alarms a day and the nightmare that would create.
If you want to be really careful, just stuff the ring in your wallet before you go through the metal detector. The wallet will not go through the metal detector. It'll go through the x-ray machine. Sure, the security will know you are about to propose, but your GF won't.