Soak 8 (8 to 12-inch) wooden skewers in water to cover for at least 30 minutes.
In a large bowl or plastic container, mix together the orange juice, lemon or lime juice, orange zest, garlic, olive oil, basil, and salt and pepper until well blended. Add the shrimp and toss in the mixture to coat. Let sit at room temperature for 15 minutes, or refrigerate for 1 to 4 hours.
Preheat the broiler or grill. Skewer the shrimp, dividing them evenly between the skewers. Discard any remaining marinade. Broil or grill for about 4 minutes total, turning as they brown, until they are just cooked throughout.
If they get a nice soak in the marinade the get so flavorful that you don’t even need to think about a dip, which is music to many of our ears. But don’t let them marinate for too long, as the acid in the lemon juice will start to change the texture of the shrimp. And it bears repeating every once in awhile – don’t over cook those shrimp.