Bring the the 3 C of pitted and halved cherries and 1/4 C of water to a boil over medium heat, and then reduce the heat and simmer until the cherries soften and release their juice--about 5-10 minutes.
Using a jelly bag and stand or old clean pillowcase tied to a cabinet know , strain the juice out of the berries. Allow juices to drain for at least 30 minutes or until the dripping stops, then squeeze the bag to release every bit. (note: wear clean rubber or plastic gloves unless you want red hands for a day!)
Juice the limes and add to the cherry juice. Measure the juice and add the same amount of sugar. (ie 2 1/4 C of juice would have 2 1/4 C of sugar)
Bring sugar/juice mixture to a boil while stirring to dissolve sugar. Cook for several minutes until the mixture becomes thicker and reduces a bit. (note-taste at this point--if you want more lime, add it)
You may either can the syrup using 1/4 inch headspace and processing for 10 minutes in a boiling water bath, freeze for 6 months or refrigerate for 2 weeks.