In a small saucepan, combine blackberries, sugar, water, and sage leaves. Bring to a simmer over medium heat, stirring occasionally, until the berries break down and the sugar dissolves, about 5 minutes.

Remove from heat and let steep for 10 minutes. Strain through a fine-mesh sieve into a bowl, pressing on the solids to extract as much liquid as possible. Discard solids.

Stir in the apple cider vinegar. Taste and add more vinegar if desired. Let the syrup cool completely.

Fill two tall glasses with ice. Divide the syrup evenly between the glasses (about 1/3 cup each).

Top with sparkling water and stir gently to combine. Garnish with fresh sage leaves and a few blackberries if desired. Serve immediately.