If using fresh cherries, remove stem and pit.
Bring to a boil, in a large nonreactive pot, the cherries, cinnamon and water. Cook at a low boil, until cherries have lost their color, 15-20 minutes. If you are using frozen cherries, reduce water to 3 3/4 cups and cook for only 10 minutes.
Remove cinnamon stick and discard.
Drain cherries, reserving the liquid. Reserve liquid and set aside half the cherries.
Puree remaining cherries and reserved liquid in batches with blender, food processor or stick blender. Return to pot.
Add lemon juice, sugar or honey, and the cherry liqueur or wine. Reheat and add remaining cherries.
Serve hot or chilled, topped with a dollop of whipped cream, sour cream or yogurt.