Fill a dish with water and soak skewers for 30 minutes.

Preheat an outdoor grill for medium heat and lightly oil the grate.

Thread shrimp onto skewers; place on a large serving dish. Brush skewers with 1 ounce pesto.

Grill shrimp skewers on the preheated grill until they are bright pink on the outside and the meat is opaque, about 4 minutes per side. Brush cooked shrimp with 1 ounce pesto. Sprinkle with basil and serve with remaining pesto and lemon slices.