So, I went through and found that the tiara was set to self-illuminating. On further inspection, I found that literally everything in the scene was set to self-illuminating, including Victoria 4. Why, I don't know, but I didn't set them that way myself.

Anyways... Disabling that still didn't result in shadows. I did about a dozen different renders, with the light positioned in different locations, with and without IBL, etc. Nothing was working. So I'm wondering if maybe it's just something flawed in how the item was created?

In any case, I won't be using that for close-up renders. It looks like I did a sloppy job of Photoshopping it into the image and forgot to create a drop shadow.

Beyond that, I'm at a loss.