Stir together the cherries, ½ cup water, and sugar in a medium saucepan. Turn to medium-high heat and bring to a low boil, stirring occasionally. Cook for 5 to 7 minutes, until the cherries soften, but remain mostly whole, and the liquid begins to thicken.

Reduce heat to medium-low. Add the liqueur. Stir together the remaining tablespoon of water and the cornstarch in a small bowl. Pour the slurry into saucepan as you stir constantly.

Continue to stir and let the compote thicken, 2 to 3 minutes. Remove from the heat and let cool before serving. The compote can be stored in the refrigerator up to 3 days.