Using kitchen shears, cut the top of the lobster shells lengthwise down the center.
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 5-6 minutes, then flip and grill for another 4-5 minutes until the meat is opaque and slightly charred.
Remove from the grill and serve with additional melted butter and lemon wedges if desired.