How to Make It
Working in batches, puree the cherries in a blender or food processor. Pass the juice through a fine sieve, pressing hard on the solids to extract as much juice as possible.
In a large saucepan, combine the cherry juice with the sugar, water and lime juice and bring to a boil, stirring constantly, until the sugar is dissolved. Cook over moderate heat for 10 minutes, skimming off the foam that rises to the top with a slotted spoon. Reduce the heat to moderately low and simmer, stirring and skimming occasionally, until syrupy, about 1 hour. Strain the syrup into jars and let cool completely before storing.