I'm working on culturing marine algae and notice the use of Boveri dishes in older papers. However, I can't find a description anywhere on the web. Supply companies don't seem to have them either.
Given the usage, I was assuming they might be deeper, maybe narrower petri dishes. I'm using pyrex food containers with petri dishes for lids. Hopefully that will work.
I think they are a little deeper than a regular petri dish. So, a regular petri dish will probably work for you unless you want it much deeper; then use a crystallizing dish.