Salt and boil a large pot of water.
Add the lobster tails and boil 3 to 5 minutes, depending on size.
Remove and drain well.
With the underside of the tail facing up, make a lengthwise cut through the tail meat, but not through the upper shell, or the tail fins. The upper shell will act as a hinge buy keeping the tail in one piece, while exposing tail meat.
Heat a charcoal or gas grill to medium-high heat.
Brush the lobster flesh with drawn butter, and sprinkle with salt and pepper.
Place the tails flesh-side down on the grill and cook over direct heat until slightly charred, about 3 minutes.
Turn the tails over so the flesh side is facing up, and brush with melted butter. Grill for 2 to 3 minutes more, brushing once or twice with melted butter.
Remove tails to a platter and top with more butter.