Combine the marinade ingredients in a medium bowl.
Place the shrimp and artichokes into a half-gallon storage bag. Add all but 1/3 cup of marinade to the shrimp. The reserved marinade can be used as a dipping sauce when serving. The shrimp should marinate for at least 1 hour, and no more than 2 hours.
After marinating, thread the shrimp and artichokes onto the skewers, 3 shrimp and 3 artichoke halves per skewer.
Position the oven rack in the middle slot with the rack oriented upwards. Preheat your Calphalon XL Convection Oven for 5 minutes on Broil. Place the skewered shrimp into the convection oven and broil the shrimp for 2 to 3 minutes on each side. Serve with dipping sauce. Serves 3 to 4 as an appetizer.