Reliquary, not Shrine ...

So, it turned out, that what I was looking for, or meant to be looking for, was in fact reliquaries, and not shrines. Thank you, dear wife, for the tip on that :)

With that sorted out, it was much easier to find the stuff I was looking for, that had the look and function that I'm trying to resemble in my piece.

Interestingly, but maybe not surprisingly, I also found reliquaries made by contemporary artists. Here are some examples of both, with the two last ones being contemporary art.