In a large saucepan over medium-high, bring cranberries, grapes, sugar, and 1/2 cup water to a boil. Reduce heat, and simmer until most of the cranberries have popped and grapes are falling apart, 10 to 15 minutes.
Remove from heat; add salt and stir to combine. Let cool to room temperature (compote will thicken as it cools). Serve at room temperature.
Refrigerate in an airtight container up to 2 weeks.