Rinse the cherries in cold water. Removed the excess water with a salad spinner or towel. Remove all leaves and stems.
Heat 1/2 cup of water in a clean saucepan until wisps of steam come off the top. Stir in the sugar until it dissolves completely. Remove from the heat.
Pour the cherries and the anise seeds into a one-gallon glass jug with a tight-fitting cap. Add the simply syrup from step 2 to the jug. Cap the jug tightly and shake it like crazy for about five minutes.
Add the vodka and shake to blend. Cap the jug loosely, so air an get out, and store it in a cool, dry, dark place for a few months. (Mark the date on the bottle so there will be no doubt.)
After at least two months, strain the contents of the jug through cheesecloth or a coffee filter set into a clean sieve. (The latter will take a long time; the bigger the filter, the better.)
Serve as a digestif with coffee. Have something else ready as an after-dinner drink in case some don't like it--an inevitability.