In a medium sized saucepot, combine pitted cherries, sugar, and lemon juice. Place over medium-high heat and bring to a boil, stirring occasionally to keep the bottom from scorching. If you're using frozen cherries, you don't need to defrost them.
Once it starts boiling, reduce your heat to medium-low and simmer for 5 to 10 minutes, or until softened to your liking.
In a small bowl, whisk together your water and cornstarch until it forms a smooth and thick mixture. Slowly drizzle the cornstarch mixture into the cooked cherry mix, stirring constantly to prevent clumping.
Continue cooking until the mixture boils and thickens to your liking. If using frozen cherries, it may take slightly longer to thicken because they do have more moisture than fresh cherries. Cool and serve!