Combine a ½ cup of sugar and a ½ cup of water in a small saucepan. Bring the mixture to a boil.
Once boiling, reduce to a simmer. Let it simmer for 10 minutes.
Remove the mixture from the heat and add in a handful of rosemary sprigs. Let the rosemary infuse into the mixture for 15 minutes.
Once the simple syrup has cooled down, remove the rosemary sprigs from the mixture and store the simple syrup in a cruet.