For the rosemary syrup: Place the rosemary leaves in a heatproof container. Pour boiling water over the leaves, cover, and let steep for 15-20 minutes.
Strain the rosemary-infused water into a clean container, discarding the leaves.
While the infusion is still warm, stir in the honey until completely dissolved. Allow the syrup to cool completely.
For the grapefruit juice: Cut grapefruits in half and juice them using a citrus juicer or reamer.
Strain the freshly squeezed juice through a fine-mesh sieve to remove pulp and seeds.
To assemble the non-alcoholic sparkler: Fill tall glasses with ice cubes.
For each glass, add 2 tablespoons of rosemary syrup and 1/4 cup of grapefruit juice.
Top with 2 ounces of sparkling water and gently stir with a long spoon to combine.
For the alcoholic version: Add 1.5 ounces of vodka, gin, or white rum to each glass before adding the sparkling water.
Garnish each glass with a sprig of fresh rosemary and a thin slice of grapefruit on the rim.
Serve immediately to enjoy the best taste and effervescence.