Give this recipe a try:
Grilled Lobster with Rosemary Butter
Prep: 15 minutes Grill: 12 minutes
Makes: 4 servings
4 8-ounce frozen lobster tails
2 teaspoons olive oil
1/2 cup butter, preferably unsalted
4 teaspoons finely shredded orange peel
2 rosemary sprigs
1 medium orange, cut into wedges (optional)
1. Thaw lobster. Rinse lobster, pat dry. Place lobster, shell sides down, on a cutting board. To butterfly, with kitchen scissors cut each lobster in half lengthwise, cutting to but not through the back shell. Bend backward to crack back shell and expose the meat. Brush lobster meat with oil.
2. If using a charcoal grill, grill lobster, shell sides down, on the greased rack of an uncovered grill directly over medium coals for 12 to 15 minutes or until lobster meat is opaque and shells are bright red, turning once halfway through grilling. (If using a gas grill, preheat grill. Reduce heat to medium. Place lobster, shell sides down, on greased grill rack over heat. Cover and grill as above.)
3. While lobster is grilling, melt butter with orange peel and rosemary over very low heat without stirring; cool slightly. Pour the clear, oily layer through a fine sieve into a serving dish, discarding the milky layer, orange peel, and rosemary. Serve with lobster; store any remaining butter covered in refrigerator up to 1 month. If desired, serve lobster with orange wedges.