Use a potato masher to coarsely crush the berries in a medium bowl. Pour mashed berries into a 2- to 3-quart pan and set over medium-high heat. Add remaining ingredients.
Bring mixture to a boil, then simmer, uncovered, until the berries cook down to a purée and turn bright red, about 20 minutes.
Pour mixture through a fine strainer and press any solids to extract all the juices; you should have about 1 1/2 cups (if the mixture is too thick, thin with water). Serve syrup warm or at room temperature.
Note: Nutritional analysis is per 1-tablespoon serving.