Rinse the fresh Stone Crab claws off with cool water. Making sure there is no oceanic debris still lingering.
Fill a large pot with about 1.5 inches of water, making sure the water is below where the steaming basket will sit.
Place the steaming basket into the large pot and cover the pot with a lid.
With the lid on the pot, bring the water to a boil over high heat. Covering the pot will make the water boil quicker and keep the steam contained.
Now that the water is boiling quickly remove the lid and drop the prepped Stone Crab claws into the basket and re-cover the pot with the lid. Be careful to not let too much of the heated steam to be released.
Keeping the water boiling and the lid on the pot, steam the crab claws for about 5 minutes.
Once the 5 minutes are up, immediately remove the claws from the pot by either using tongs or if your steaming basket has a handle, simply lift the whole thing out of the pot and off the heat.
Crack the claws and remove the meat while warm, to ensure you get all of the meat out of the shell with little to none sticking to the claws shell.
Now, you can serve them while warm or you can chill them and serve them cold with some sort of dipping sauce. Melted butter or a mustard sauce are the preferred sauces for Stone Crab claws.