In a small saucepan over medium-high heat, bring the water, sugar, rosemary, and salt to a simmer. Reduce the heat to maintain a gentle simmer and cook, uncovered, stirring often, for 2 minutes.
Remove from the heat and let sit for 30-60 minutes. This allows the rosemary to more fully infuse the syrup. Remove rosemary and discard. Transfer to a jar and refrigerate until ready to use.
Notes
Storage: The rosemary simple syrup will keep in the refrigerator for at least 2 weeks.Scaling up: The recipe can easily be doubled or tripled. It is harder to scale the recipe down, as there may not be sufficient liquid to cover the rosemary. If you'd like to try, a pot that's small and deep will work the best.