Muddle the blackberries and water together until well pulverized. Strain the juice from the pulverized berries (should yield ¼ - 1/3 cup juice).

In a small pitcher, combine the blackberry juice, lime juice, tequila, orange liqueur, and simple syrup and stir together. Add the mixture to a cocktail shaker and shake for 30 seconds. Pour in chilled glasses rimmed with salt or sugar. Garnish with lime wedge.