In a large bowl, stir together garlic, olive oil, and tomato sauce.
Season shrimp with basil, salt, and cayenne pepper.
Add shrimp to the bowl, and stir until evenly coated.
Cover, and refrigerate for 30 minutes to 1 hour, stirring once or twice.
Heat grill to medium; lightly oil grill grate.
Thread shrimp on skewers; pierce once near head and once near tail.
Place shrimp on preheated grill.
Cook 2 to 3 minutes per side or until opaque.
Note: Unused sauce goes well tossed with Cavatappi noodles, a little sour cream, and Mozzarella cheese.