In a small saucepan, combine the blackberries, 1 cup of water, and sugar (or honey).
Bring the mixture to a gentle boil over medium heat, stirring occasionally until the blackberries have broken down and the mixture has thickened slightly (about 5-7 minutes).
Remove from heat and add the sage leaves to the mixture. Let it steep for about 10 minutes to infuse the sage flavor.
Strain the blackberry mixture through a fine mesh sieve into a pitcher, pressing down on the solids to extract all the juice, then discard the solids.
Add the fresh lemon juice and 1 cup of cold water to the blackberry-sage syrup, stirring well to combine. Adjust sweetness if necessary by adding more sugar or honey to taste.
Serve over ice cubes in tall glasses, garnished with lemon slices and a few blackberries.
For an extra touch, add a sprig of fresh sage to each glass just before serving.