Combine 2 cups blueberries, 1 cup water, kumquats, sugar and juices in a medium heavy-bottomed saucepan. Bring to simmer over medium-low heat.
In a small bowl, stir cornstarch and 2 tablespoons cold water until well combined. Slowly pour into the hot blueberry mixture and continue to simmer until thickened, 4 to 6 minutes.
Gently stir in remaining 3 cups blueberries and blackberries into thickened mixture and simmer gently over low heat for 3 minutes. If too thick, add up to 4 tablespoons cold water. Stir in pepper and remove from heat. Transfer to clean containers and store in the refrigerator for up to 2 weeks.
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