Professor being mistaken for a grad student This question is the flip side of Mistook new faculty member to be a student, how big a faux pas is it?

I'm an associate professor, and apparently I look young for my age. When I meet new people at conferences, they often start the conversation with something like  "So, are you a grad student or a postdoc?"  It doesn't particularly bother me in itself, but when I politely say something like "Actually, I'm faculty", they get embarrassed and it kind of puts a damper on the conversation.  I think this sort of thing has probably spoiled a few potential networking opportunities for me.


Are there more tactful ways I can respond to this kind of mistake?
Are there things I could do to "look" more like a professor?  I already dress reasonably neatly (e.g. no T-shirts) and faculty in my field don't normally dress up much more than that.  Should I carry a briefcase instead of a backpack, or something like that?


(I happen to be cis male, work in mathematics, and live in the US, but it would be good to have more generally applicable answers if possible.)
I would take it as a compliment to be mistaken for being younger. And, even if you don't actually feel complimented, that's a good way to respond. For example, you could laugh and say "Thanks. I wish I was still a young and carefree student, but, unfortunately, I'm a professor." 

If you make it appear like you take it as a compliment, people won't feel like they have offended you and it is less awkward. The other party may also intentionally be erring on the side of underestimating your age, because it's seen as less of a faux pas that way.

(I often get people commenting on my height. I always act as if I take it as a compliment and that seems to work well. However, in reality, I'm pretty bored of discussing my disinterest in basketball.)

At conferences, you always have the option of putting "Prof." on your nametag. There is a small risk that this looks pretentious relative to the norms of your community, so it's a tradeoff. 

Finally, there is one sure-fire way to appear older.