Put the lobster tails on a baking sheet. With a sharp knife or kitchen shears, cut the top side of lobster shells lengthwise. Pull apart shells slightly and pull the meat out and over the shells, but leave attached.
Season the meat with the melted butter, paprika, salt, and pepper.
Turn broiler down to low before putting in the tails. Broil on low for 10 to 15 minutes, keeping a close eye so they don’t burn. The meat should be opaque and slightly browning when done.