Place the kumquats in water for three days, changing it daily.

Boil them in water that covers them for 30 minutes.

Discard the boiled water and boil once more for an additional 30 minutes.

Discard the water again and check if they are tender enough to pierce with a toothpick. If the peel is hard make a few holes with the toothpick.

Prepare the syrup using as much sugar as is the weight of the kumquats + 250 g. So, for half a kilo of kumquats use 750 g of sugar. Add 1 1/2 cup of water, boil for 2 minutes and towards the end add a few drops of lemon juice. 

Add the boiled fruits into the syrup and boil them together for a few minutes.

If the syrup thickens too much add a little water and boil for 5-6 minutes.

If the syrup is too thin add some sugar on the next day and boil for 3-5 minutes.