You can strain the syrup left after making kumquat slices to flavor iced tea or lemonade.
Cut kumquats into 1/8-inch-thick slices. Stir together 1/2 cup sugar and water in a small heavy saucepan. Bring to a boil over medium heat. Reduce heat to medium-low, and stir in kumquat slices; simmer 10 minutes. Remove from heat; remove kumquat slices, 1 at a time, shaking off excess sugar-water mixture. Place kumquats in a bowl with 1/4 cup sugar; toss to coat. Transfer kumquats to wax paper. Cover loosely with plastic wrap, and let stand 24 hours.