What is a good way to hold a buttplate while polishing it?
You can polish the buttplate right on the stock by clamping the stock in a vise, though the stock can be a bit cumbersome to manipulate that way. Another option is to cut a block of wood to the shape of the buttplate and attach the plate to it with small screws, taking care not to over tighten the screws so the plate does not distort.