Start a charcoal or gas grill, or heat the broiler. Make the fire as hot as it will get, and put the rack close to the heat source.

Mince garlic with salt; mix with cayenne and paprika, then make into a paste with olive oil and lemon juice. Smear paste on shrimp. Grill or broil shrimp, 2 to 3 minutes a side, turning once. Serve immediately or at room temperature, with lemon wedges.