Slice ends off kumquats and discard. Then slice each fruit into 4 slices each, removing seeds as you go.
Bring water and sugar to a boil in a saucepan large enough to also accommodate the kumquats.
When the water is boiling and the sugar is dissolved add the kumquats.
Simmer for 10 minutes, gently stir occasionally.
Drain the kumquats over a bowl and return the syrup to the saucepan.
Bring the syrup to a boil once again and cook until reduced by about half.
Put the fruit slices into a bowl or jar and pour the syrup over. Cool, then cover and refrigerate.