Rinse clams several times in cold, running water. Soak them in salted or seawater with a few handfuls of cornmeal for 15 minutes. Drain and rinse again.
Fill a steamer with 1-inch cold water, celery and parsley and bring to a boil. Add clams all at once. Bring back to a boil, then cook for about 4 minutes, shaking the pot from time to time, until clams open. (If you wish, cook 3 to 4 minutes longer, to kill off harmful bacteria that may exist.)
Remove steamers with a spider or a large slotted spoon to serving bowls. Open spigot of steamer and strain broth into small bowls for serving. If your steamer does not have a spigot, ladle broth into bowls, leaving behind any debris. Serve steamers immediately with broth and hot melted butter for dipping.
Recipe courtesy of David Rosengarten