How to Make It
Combine granulated sugar and water in a medium saucepan, and bring to a simmer over medium high, stirring until sugar dissolves. Add lime slices, and simmer 5 minutes. Remove limes with a slotted spoon to a small bowl. Add cranberries to pot, and simmer 1 minute. Transfer to a medium bowl, and let cool to room temperature. Drain cranberries well, and discard or reserve liquid for another use. Drain fruit well. Reserve liquid for another use. Place fruit on a rimmed baking pan and let set until almost completely dry, about 1 hour.
Toss fruit in superfine sugar to coat completely. Use immediately.