Stir together berries, sugar, zest, and juice in a slow cooker. Cook on High until bubbling, about 1-1/2 hours.
Stir together cornstarch and water in a cup until fully dissolved. Stir into berry mixture. Cook, covered, until thickened, 5 to 10 minutes more. Serve warm or room temperature.
You can also use fresh berries or stone fruit if that is what you have on hand. Great over ice cream or angel food cake.