Gather the ingredients.
Fill a large bowl with cold water. Squeeze juice from one lemon wedge into the water. Trim tops and stems from artichokes, cut in half lengthwise, and use a spoon to scoop out the fuzzy choke. Place artichoke halves in the lemon water to prevent browning.
Bring a large pot of water to a boil. Add artichokes to boiling water, and cook until tender, about 15 minutes. Drain. Meanwhile, preheat an outdoor grill for medium-high heat.
To make the basting and dipping sauce: Squeeze remaining lemon wedges into a medium bowl; stir in olive oil and garlic, and season with salt and pepper.
Brush artichokes with a coating of lemon-garlic dipping sauce; place on the preheated grill and cook, basting with sauce and turning frequently, until the tips are a little charred, 5 to 10 minutes. Serve immediately with remaining lemon-garlic sauce.
