Peel and break up the orange or grapefruit into segments. Divide the segments among 4 pint-size containers. Add one or two ½-inch orange peel segments to each bottle.
Fill each container with kombucha, leaving about ½ inch of headspace. Seal tightly.
Place in a warm spot out of direct sunlight for 3 to 10 days. Burp the containers daily to release excess pressure and check for carbonation. If not sufficiently carbonated, reseal the containers, give them a quick shake, and continue to ferment for up to 10 days.