Build the box around the slate.
here are videos how to make shadow boxes https://www.youtube.com/results?search_query=diybuild+your+own+shadow+boxes
Hi! I found a cool tutorial on making a box from slate tiles, attaching them, etc. Hope it helps:
I have a couple of slates like that. I never thought about making a shadow box but I would think the best way to do it is to make a groove in the wood, where it fits tight into the box, so that it won't fall out.