Place lemon and orange peel in water to cover in a large saucepan; bring to a boil. Boil 20 minutes; drain. Set aside.
Combine 2 cups sugar and water in a medium saucepan; bring to a boil. Cook until mixture reaches thread stage (230°). Add peel; reduce heat, and simmer 5 minutes, stirring frequently. Drain well.
Roll peel, a few pieces at a time, in sugar. Arrange in a single layer on wire racks; let dry several hours. Store in an airtight container.