Straining the blackberry mixture is optional but worth the effort for the smoothest, creamiest texture.
Combine blackberries and sugar in a blender or food processor; process until smooth. Strain blackberry mixture through a fine sieve over a bowl; discard solids. Stir in buttermilk.
Pour mixture into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Spoon sherbet into a freezer-safe container; cover and freeze 4 hours or until firm.
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