In a heavy saucepan, boil the cherries with 1 cup water until they become very soft. Over a bowl, strain the liquid through a sieve lined with muslin or several layers of cheesecloth. When most of the juice has drained, gather up the edges of the cloth and squeeze the remaining pulp to extract as much liquid as possible. Discard the pulp.

Put the sugar and 1 cup water into the saucepan, bring to a boil, and reduce the heat. Simmer for 5 minutes, then add the cherry juice. Return to a boil, stirring constantly, then lower the heat and simmer very gently for 5-10 more minutes, until the syrup is the consistency of maple syrup. Turn off the heat and let the syrup cool. To serve, pour 3 tbsp. of syrup into a glass, then add ice water and stir well.