In a large bowl, combine the olive oil, minced garlic, lemon juice, salt, and black pepper.
Add the shrimp and toss until evenly coated.
Cover and marinate for at least 15 minutes.
Meanwhile, preheat your grill to medium-high heat.
If using wooden skewers, soak them in water for 15 minutes.
Thread the shrimp onto the skewers.
Place the skewers on the hot grill.
Grill the Pesto Grilled Shrimp Recipe for 2–3 minutes per side, basting with any remaining marinade as they cook.
During the last minute of grilling, brush the shrimp generously with basil pesto.
Remove from the grill and garnish with fresh basil leaves.
Serve immediately with fresh lemon wedges.