In a pot, combine sugar with 75 ml (approximately 1/3 cup) water. Bring to a boil and simmer until sugar has completely dissolved.
Rinse oranges with hot water, cut in half and squeeze juice.
Scoop out remaining orange flesh with a spoon. Freeze orange halves.
Juice grapefruits, measuring 550 ml (approximately 2 1/3 cups) of the juice. Mix grapefruit and orange juices with sugar syrup.
Pour mixture into a shallow baking dish and place in the freezer. When the liquid begins to freeze at the edges, stir with a whisk or fork.
Freeze 4 hours, breaking up ice crystals with a whisk or fork occasionally. To serve, fill frozen orange halves with granita and spoon Campari over the tops.