Run the clams under cold water and scrub clean with a brush. Rinse and set aside.
In a large stockpot, add wine and bring to a boil over medium-high heat. Gently add clams to the boiling wine, cover and steam until fully opened, about 5 minutes.
While the clams are steaming, melt butter on stovetop or in microwave and add the minced garlic. Place into small serving bowls.
Serve immediately with lemon wedges and pour some of the hot broth in each bowl.