Preheat the grill to medium-high heat.
Using kitchen shears, cut the top shell of each lobster tail down the middle.
Gently pull apart the shell and loosen the meat without detaching it.
In a small bowl, mix melted butter, garlic, lemon juice, paprika, salt, and pepper.
Brush the garlic butter mixture over the lobster meat.
Place lobster tails flesh-side down on the grill and cook for 5 minutes.
Flip the tails, baste with more garlic butter, and grill for another 4-5 minutes until opaque.
Remove from grill, garnish with fresh parsley, and serve with lemon wedges.