Preheat your grill to medium-high heat.
In a small bowl, combine melted butter, minced garlic, lemon juice, paprika, salt, and pepper.
Using kitchen shears, cut the top of the lobster shell lengthwise from the outside, being careful not to cut the meat. Pull apart the shells slightly and brush the lobster meat with the butter mixture.
Place the lobster tails flesh side down on the preheated grill for 5 minutes. Turn them over and grill for another 3-5 minutes, or until the lobster meat is opaque and cooked through.
Remove from the grill, garnish with chopped parsley, and serve immediately with extra lemon wedges on the side.