I don't know about other women, Anonymous, but I find that compliments to my appearance can be both flattering and hard to accept. Maybe the best compliment I've ever received wasn't a compliment at all, but someone commenting offhandedly that I had a nice smile, that I should laugh more because it's beautiful. I think that it's always nice to hear someone say that you look nice, you look beautiful, you look pretty, your hairstyle is neat, whatever compliment like that about one's own physical appearance or style. If you can find something about the person you want to compliment that's more about who they are, though, like how you're amazed at how well they can play the piano or the way they laugh or even just how polite they are or how kind they are to others, that's probably more optimal if you're looking for a different route.

This is just from this girl's perspective, though.