Start the syrup by combining the blackberries and sugar in a small saucepan. Squish the berries to release some of their juices and put the pan over medium low heat. Let the berries liquidate, their juices coming to a boil, before lowing the heat to a simmer for 5 minutes. Give the berries another smooshing to make sure they’re all broken up. Let the syrup cool for about 30 minutes before straining into a small jug through a fine mesh sieve to catch all the seeds.