Set up an ice bath and a wire rack set over a baking sheet or parchment paper.
Using a mandolin, cut limes into ⅛-inch slices. Discard seeds and the ends.
To a saucepan set over high heat, add water and bring to a boil. Turn off heat and add lime slices, stir gently until softened, about 1 minute. Remove lime slices from water and immediately transfer to ice bath.
To a saucepan set over medium-high heat, add sugar and 1 cup of water, bring to a boil. Stir gently to dissolve sugar. When mixture is boiling, reduce heat to medium-low and add lime slices, arranging in one layer. Simmer gently until rinds are translucent, 45 to 60 minutes.
Carefully transfer lime slices to the wire rack. Let set for at least 1 hour or until the slices have hardened slightly and are no longer sticky.
