Halve and squeeze the lemon and oranges, measure 800 ml orange juice. Wash kumquats, dab dry and cut into thin slices. Mix orange and lemon juice, Cointreau, jam sugar, kumquats and cardamom in a large pot.
Bring to the boil over a high heat, stirring continuously, and let it boil for 1 minute until it becomes bubbly. Immediately fill jam into clean glasses and close them. Turn upside down for about 5 minutes.