Using kitchen shears, cut the top of the lobster shells lengthwise down the center. Pull apart shells slightly, and season the meat with salt and pepper.
In a small bowl, mix melted butter, garlic, lemon juice, and paprika.
Brush the lobster meat with the butter mixture.
Place the lobster tails on the grill, meat side up. Grill for about 10 minutes, or until the lobster meat is opaque and firm to the touch.
Remove from the grill and serve immediately with additional melted butter if desired.