Scrub the clams, and rinse clean. Bring 2 cups of water to a boil in an 8-quart stockpot over high heat. Add the clams, and cover tightly. After 5 minutes, uncover, and stir the clams with a wooden spoon. Quickly cover the pot again, and let steam for 5 minutes more, or until most of the clams have opened. Don't wait for them all to open, or they will be overcooked. It should only take a little tug or prying to open the stragglers once they are all removed from the heat. The total cooking time for large cherrystones will be about 10 minutes; quahogs will need as much as 5 more minutes. While the clams are steaming, the broth should become foamy and light. It usually spills over a bit just as the clams are cooked and ready.
As soon as you remove the clams from the stove, carefully pour as much of the broth as you can into a tall, narrow container. Let the broth sit for 10 minutes, then carefully pour through a fine-mesh strainer. After sitting, 99 percent of the grit will have collected at the bottom of the container. If you are not using the broth within the hour, chill it as quickly as possible, and cover after it has completely cooled.
Remove the clams from their shells, cover, and refrigerate. After they have cooled a bit, dice them into 1/2-inch pieces. Cover again, and keep refrigerated until ready to use.
Keep refrigerated for up to 3 days.