Rinse blackberries and place in a food processor. Process until completely pureed. Add sugar and combine.
Pour the blackberry mixture into a fine wire sieve and press it through with back of a wooden spoon to remove all the seeds.
To make the drink, place 1 - 1 ½ tablespoon of the blackberry puree in the bottom of a champagne flute and top with ginger ale for a non-alcoholic version. Garnish with a fresh blackberry.