Prepare the rosemary simple syrup by combining granulated sugar, water, and 4 rosemary sprigs in a small saucepan over medium heat.
Bring the mixture to a gentle boil, stirring occasionally until the sugar is fully dissolved.
Reduce the heat to low and simmer for 5 minutes, then remove from heat and let the rosemary steep in the syrup for 20 minutes to infuse the flavor.
Strain the syrup through a fine-mesh sieve into a clean glass jar, discarding the cooked rosemary, and allow it to cool completely in the refrigerator.
In a small pitcher, whisk together the unsweetened cranberry juice, lime juice, and 4 tablespoons of the chilled rosemary simple syrup.
Place ice cubes and frozen cranberries into four highball glasses or festive tumblers.
Divide the cranberry base evenly among the four glasses, filling each about halfway.
Top each glass with 1/2 cup of lime-flavored sparkling water and stir very gently with a long spoon to combine without losing carbonation.
Garnish each glass with a fresh rosemary sprig and serve immediately while cold.