Bring sugar and water to a boil in a small saucepan, stirring to dissolve sugar. Add lime slices and simmer until translucent, about 6 minutes.
Remove from heat; transfer slices to a wire rack set on a rimmed baking sheet and reserve syrup. Let lime slices dry and syrup cool before using, at least 20 minutes.
Lime rounds and syrup can be stored in the refrigerator up to 1 week.