D.B.
A lot of runners (who never carry ID) wear a runner ID bracelet. It doesn't look at all like a medical bracelet. My son and husband wear them, and we got one for my mother when she was starting to have memory issues. She always considered it an "athlete's ID" rather than an "old lady tracker" and it worked fine. Most are wristbands but you can get something that attaches to the shoelaces if it won't be in her way and something she'll take off. You could also try sewing an ID label into her coat (even if it's a camp-type label for identifying kids' clothes for overnight camp). She might not notice it or perhaps she would consider it a hedge against a lost coat vs. a lost person. You could also get an engraved metal tag like a dog license (just get one that's a heart shape, not one that's a dog bone shape) and put it on as a zipper pull or inside the coat where they attach the extra buttons. Put her name/address and your contact number on it.
These don't help you find her, but they do help the police locate you.
