Peel shrimp, then cut each down the back, from neck to tail, almost all the way through. Pull out and discard veins. Rinse shrimp and lay open, cut sides down, pressing gently to flatten. For easier handling and to hold shrimp flat, run thin metal skewers, in parallel pairs, crosswise through shellfish, filling skewers.
In a 6- to 8-inch frying pan over low heat, stir butter and garlic occasionally until butter melts, about 4 minutes.
Remove from heat.
Mix or brush shrimp with 2/3 cup of the butter mixture.
Lay shrimp, spread open, on a barbecue grill over a solid bed of hot coals or over high heat on a gas grill (you can hold your hand at grill level only 2 to 3 seconds). Close lid on gas grill. Cook, turning once, until shrimp are opaque but still moist-looking in thickest part (cut to test), 5 to 7 minutes.
Transfer to a platter as cooked.
Warm remaining garlic butter and spoon over shrimp.
Add salt and pepper to taste. Squeeze lime onto shrimp to taste.
