A trophy case combines fragile glass panels with irreplaceable awards inside, so the entire move is about emptying it completely and protecting both the case and its contents separately.
Pro tip: Photograph the entire trophy display before disassembly, since many school trophy cases represent years of accumulated history that nobody wants to guess at reassembling.
Watch out: Never move a trophy case with trophies or glass shelves still loaded; the shifting weight is a leading cause of cracked glass panels and toppled displays during a move.