Bring the sugar and water to a simmer. Allow to simmer for 5 minutes. Cool completely.
Place the kumquats in a clean jar with a tight fitting lid. Pour the cooled syrup over the kumquats. The kumquats are buoyant and need to be weighted down. I place a piece of parchment paper over them and weight it down.
Place the kumquats in the refrigerator and in 3 weeks the kumquats will have softened and will be sweet and slightly sour. Store the kumquats in their syrup for 2-3 months.