1. In a large bowl, whisk together lime juice, olive oil, ginger, brown sugar, garlic, lime zest, and sesame oil. Set aside.
2. Peel and devein the shrimp, leaving the tails intact. Add shrimp to marinade and toss to coat thoroughly. Cover bowl or place contents of bowl in large resealable plastic food storage bag and refrigerate for at least 1 hour.
3. Preheat grill or broiler. Thread shrimp and lime wedges onto 8 skewers, dividing evenly.
4. Cook shrimp skewers directly over medium-hot fire for about 5 minutes or until shrimp are bright pink, turning once during cooking. Or cook directly under the broiler, 3 to 4 inches from the heat source.