Using a sharp knife, halve each tail lengthwise, cutting all the way through the shell.
Heat your outdoor grill or grooved stovetop griddle to high heat. Place lobster tails shell side down on grill. Baste with melted butter and cook until the meat becomes opaque white and the shell turns bright red.
Turn over lobster tails so that the meat side is facing down on grill. Cook until brown grill marks appear on lobster meat, about 30 seconds. Serve immediately.