Using kitchen shears, cut the top of the lobster shells lengthwise down the middle to the tail, and pull apart the shells slightly.
In a small bowl, combine melted butter, garlic, lemon juice, paprika, salt, and pepper.
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, or until the meat is opaque and cooked through.
Remove from the grill and serve immediately with extra lemon wedges if desired.