In a cocktail shaker, combine the lemon juice and blackberries. Muddle thoroughly with a muddler (or in a pinch, the handle of a wooden spoon).
Add a handful of ice and combine the simple syrup, cointreau, cognac (or brandy), and cherry juice to the shaker. Close the shaker and vigorously shake for 30 seconds.
Take your chosen glass and fill with a few ice cubes. Set a small sieve over the glass and strain the cocktail. Garnish with fresh blackberries.