Grilling Lobster Tails indoors

I have BROILED lobster tails in the oven with good success: Heat the broiler. I slit the tail down the backside and pull the meat upward from the shell, but try not to detach. I then fold/crunch the shell back under the meat. I baste with melted butter (with or without fresh lemon juice ) and sprinkle a little paprika on top for color. Broil until the lobster meat is opaque.