Using a sturdy vegetable peeler, remove the zest from the orange, lemon and grapefruit. Cut the zest into fine julienne strips.
Fill a medium saucepan with cold water. Add the zest and bring to a boil. Remove from the heat and let stand for 15 minutes. Drain the zest and rinse under cold water.
Return the zest to the saucepan. Add 1/2 cup of the sugar and 1 cup of cold water and bring to a boil, stirring until the sugar dissolves. Simmer over low heat until the glaze is slightly thickened and the zest is softened and translucent, about 20 minutes.
Strain the glaze into a heatproof bowl, pressing on the zest to extract as much glaze as possible. Return 2 tablespoons of the zest to the glaze.
Spread the remaining 2 cups of sugar on a large plate. Scatter the remaining zest over the sugar and toss to coat completely. Scatter the sugared zest on a wax paper-lined plate and let stand until dry to the touch, about 2 hours.
The glaze and candied zest can be stored separately in airtight containers at room temperature for up to 2 days. Reheat the glaze before using.