For the blueberry basil puree: Add the blueberries, sugar, basil and 1/4 to 1/2 cup water (as needed) to the carafe of a blender. Blend until smooth. Strain through a sieve into a serving vessel. Refrigerate until ready to use or serve immediately.
For the raspberry rosemary syrup: Add the sugar, raspberries, rosemary sprigs and 3 cups water to a small saucepan over medium heat. Bring to a boil, then reduce to a simmer. Simmer until the raspberries burst, the sugar is dissolved and the liquid is bright pink, about 15 minutes. Remove from the heat and press through a mesh sieve into a bowl or large measuring cup. Transfer to a serving vessel and refrigerate until cold, about 1 hour.
For the drinks: Add the blueberry basil puree or raspberry rosemary syrup to any desired mixer. Mix and match as desired. Garnish with herbs, berries or citrus.