Fill a large bowl with cold water. Squeeze the juice from one lemon wedge into the water. Trim the tops from the artichokes, then cut in half lengthwise, and place halves into the bowl of lemon water to prevent them from turning brown.
Bring a large pot of water to a boil. Meanwhile, preheat an outdoor grill for medium-high heat.
Add artichokes to boiling water, and cook for about 15 minutes. Drain. Squeeze the remaining lemon wedges into a medium bowl. Stir in the olive oil and garlic, and season with salt and pepper.
Brush the artichokes with a coating of the garlic dip, and place them on the preheated grill. Grill the artichokes for 5 to 10 minutes, basting with dip and turning frequently, until the tips are a little charred. Serve immediately with the remaining dip.