1. Process blackberries in a blender until smooth, stopping to scrape down sides as needed.
2. Press blackberry puree through a fine wire-mesh strainer into a medium saucepan, using back of a spoon to squeeze out juice (about 1 1/2 cups). Discard pulp and seeds.
3. Add sugar and remaining ingredients to blackberry juice in pan, and bring mixture to a boil over medium heat, stirring occasionally. Boil, stirring occasionally, 1 to 2 minutes or until sugar is dissolved and mixture is smooth. Remove from heat, and cool slightly (about 30 minutes). Serve warm or at room temperature.
*1 (16-oz.) package frozen blackberries, thawed, may be substituted.