Place lobster tails on a baking sheet. With a sharp knife or kitchen shears, carefully cut the top side of lobster shells lengthwise. Pull apart shells slightly, and season meat with equal amounts of melted butter, paprika, salt, and pepper.
Turn broiler to lower setting. Broil lobster tails until lightly browned and lobster meat is opaque, about 5 to 10 minutes. Watch them closely!