Combine sugar and 2/3 cup water in a small saucepan. Bring to a boil over high heat, then let cool.
Whirl honeydew, syrup, and rose water in a blender until smooth.
Pour purée into an 8-in. square baking pan. Cover with plastic wrap and freeze until mixture starts to freeze at edges but is still slushy, 2 to 3 hours. Stir mixture thoroughly, scraping sides down. Cover and freeze until solid, at least 7 hours.
Scrape granita with a fork to make large flakes and spoon into chilled glasses or bowls.
*Find with cocktail or baking supplies.