My old hutch/china cabinet has glass shelves and it came with clear plastic holders. The back of the holder hooks over the back of the shelf and the front of it sticks up a bit to hold the bottom of the plate as the top of the plate leans against the back of the cabinet. Somewhat like a "Z" that fell forward if you look at it from the side. I've never tried to buy any, but I'm sure if you search on line you'll find something. Good Luck!

My old china cabinet has grooves etched into the glass shelves.

The open wooden shelves in my kitchen have no grooves so I use those little rubber bumper things. Works like a charm.

I got clear sticky back bumpers and lined them up along the backs of the glass shelves. Works well.

I would use a display easel (I think that's what they're called). You can find them at craft stores like Michaels. I used them to hold framed pictures at my FIL's funeral recently when I wondered how I was going to display a few framed pictures on tabletops. The ones I am speaking of do not have a flat bottom and would accomodate a plate.