I don't know where you're located, but if you're in the US, look for the craft stores, Michael's, and HobbyLobby.  They sell display cases of various styles and sizes.  Or try a sports memorabilia and collectibles dealer.  There are cases made to display baseball bats, that are a good size to display a 1/350 scale ship model.  I got that idea years ago from one of the forums, from a build of Trumpeter's USS Hornet (CV-8) in 1/350.  The modeler got a baseball bat case to display his finished model.  Note that the particular style of case was with clear sides all around, and a clear top.  There are other display cases for baseball bats that are more of a shadowbox, with solid sides all around, and only the top, or the side facing out, is clear.