Rinse and dry two navel oranges. Cut off top and bottom of oranges.
Score the skin of the oranges into four sections. Do this by making four cuts along the curve of the orange from top to bottom, cutting only through the peel.
Carefully peel the sections off taking care not to tear them. Wrap the peeled oranges and save for another use in the refrigerator. Cut remaining peel into 1/4 inch wide strips.
Place the peel strips in a large saucepan and cover with cold water. Place saucepan on stove top and bring to a boil over high heat. Once the water boils, remove from heat and drain. Refill saucepan with cold water; bring to a boil, then drain in a strainer.
In the same saucepan, stir together 1 cup sugar and 1 cup water. Place over medium heat and bring sugar water to a simmer. Cook for 5-6 minutes, or until sugar is dissolved.
Add the orange peels and cook for 45-60 minutes, keeping at a low simmer. (The peels will look translucent. Do not stir once the peels have been added as this will cause crystallization. If necessary, swirl the pan to make sure all the peels are covered with the syrup.)
Remove peels from saucepan and spread on racks to cool and drip for 30 minutes.
Place parchment paper on a baking sheet and sprinkle some of the remaining 1/3 c. sugar on the pan. Place the candied peels on the baking sheet and sprinkle with remaining sugar. Roll strips in sugar, making sure all the peel is covered.
Place in oven and bake at 170 F. for one hour. Remove from oven and let cool. Use to decorate frosted cake. (Any remaining candied orange peels will keep for two weeks in a sealed container at room temperature. Candied orange peels are good as a snack or dessert or dipped in chocolate.)