Combine water, sugar, and rosemary in a saucepan over medium heat.
Stir until sugar has dissolved.
Remove from heat and allow syrup to cool.
Once cooled, discard rosemary. Pour simple syrup through a sieve to remove any small bits of rosemary that may remain. Store in an air-tight container.
Rosemary Peach Tequila Punch
Add peaches and simple syrup into a blender and process until smooth.
Pour into a 2-quart pitcher. Add the tequila and lemon-lime soda.
Add the frozen berries and ice to a glass and pour in punch. Serve immediately.