If using wooden skewers, soak in water for at least 30 minutes before placing shrimp on the skewers. This will prevent the skewers from catching fire on the grill.
In a medium bowl, whisk together olive oil, lemon juice, garlic, honey, cayenne pepper, and paprika.
Reserve ¼ cup marinade for brushing onto shrimp while grilling.
In a large bowl, toss shrimp with remaining marinade. Cover the bowl and refrigerate. Allow the shrimp to sit in the marinade for 15 minutes up to 1 hour. Do not allow the shrimp to sit in the marinade for longer than 60 minutes or the acid will begin to cook the shrimp.
Preheat grill or grill pan to medium-high heat.
While the grill is preheating, remove the shrimp from the marinade and thread on skewers.
Grill shrimp until pink and opaque, about 2-3 minutes per side, brushing with reserved ¼ cup marinade before and after flipping the skewers.
Serve hot with lemon wedges.
Notes on Shrimp: Use frozen or fresh shrimp, with or without the tails. I prefer shrimp with the tails removed for easier eating, but the choice is yours. If you use shrimp that is are not jumbo in size keep in mind that that the cooking time will change slightly. Watch for the shrimp to be pink and opaque.Frozen Shrimp: If using frozen shrimp, thaw overnight in the fridge. Or for faster thawing, take the shrimp out of its package and place them into a sealed Ziploc bag. Submerge the bag of shrimp into a large bowl of cold water and let sit at room temperature for 15-20 minutes for the shrimp to thaw. This recipe can easily be cut in half. Grilled shrimp is best enjoyed the day it is made but can be stored in the refrigerator for up to 2 days.