Is there such a thing?
When I pulled this prompt out, I was a little confused about the idea of sentimental headgear. Unless maybe you wore braces in the '80s and had one of those contraptions that went around your head. Even then, "sentimental" implies fond feelings, and I don't think the folks who had that kind of headgear look back on it very nostalgically.
Anyway, I said all that to say that thanks to my Jeopardy experience, I had something to draw for this one. In addition to your prize money, they give you a Jeopardy baseball cap, another one of their cheap Jeopardy pens, and a super-cheap Jeopardy bag (you know, like the reusable ones from Whole Foods, except way less sturdy). I've had this cap sitting on top of a foam head ever since I got back. I was thinking about giving it to my son but I doubt he'd wear it. I know I'll never wear it.
I guess that's why I have a foam head.