Use a peeler to remove eight 5-inch strips of orange peel. Make sure to remove only the orange peel, leaving behind as much white pith as possible.
Cut each sprig of rosemary into 4-inch pieces. Remove the leaves from the bottom 1/2 inch of the rosemary sprigs, exposing the stems.
Roll up each strip of orange peel from one end to the other, peel-side out, to resemble a rose. Pierce the exposed end of the rosemary sprig through the rolled orange peel, ensuring the rosemary holds together both ends of the orange rose.
Divide the champagne among 8 flutes (about 4 ounces per glass). Top each with a splash of Campari (about 1/4 ounce). Drop a rosemary orange garnish into each flute.