Combine cherries (see notes), sugar, and water in a medium saucepan.
1 1/2 cups cherries, 1 cup sugar, 1 cup water
Bring to a simmer over medium heat and cook for 10-15 minutes. Slightly mashing the fruit with a potato masher while it is cooking can release some of the flavor, but will also result in a slightly cloudier end product. If you want a nice clear syrup, don't mash the fruit.
Remove from heat and allow to steep for 1 hour.
Strain cherries through a fine mesh strainer.
Transfer the finished syrup to a bottle or jar with a sealable lid.
Store in an airtight container in the refrigerator for a month or so.
Notes
This recipe can be made with whole cherries or pitted cherries. If you remove the pits, you'll have cooked cherry pulp leftover that can be added to muffins or other baked goods.