In the work bowl of a food processor, pulse cherries and ¼ cup (60 grams) water until cherries are puréed.

In a small saucepan, combine cherry purée, sugar, lemon juice, cornstarch, and salt. Bring to a boil over medium-high heat, stirring just until sugar dissolves. Reduce heat to medium-low, and cook, stirring frequently, until thickened, about 5 minutes. Remove from heat, and let cool for at least 15 minutes before serving. Refrigerate in an airtight container for up to 1 week.