Slice the kumquats into thin rounds across their equator, picking out the seeds as you go and setting them aside. Don't discard the seeds.
Wrap the reserved seeds in a square of cheesecloth, tie it closed, and drop the packet into your jam pot.
Add the water and sliced kumquats to the pot with the seed packet.
Let the fruit, seeds, and water soak for 3 to 4 hours so the natural pectin can draw out. This step can be skipped in a pinch, but expect a softer set and a slightly lower yield.
Bring the pot to a simmer with the lid off and cook for 35 to 45 minutes, until the fruit is soft and the mixture has started to thicken. Keep the lid off so the extra water cooks away.
Lift out the seed packet, pressing it against the side of the pot to release the gel, then stir in the sugar.
Turn the heat to high and bring the jam to a full rolling boil. Boil hard, stirring often, until it reaches gel stage at 220 degrees F or gels promptly on a plate chilled in the freezer. A gentle simmer will not reach gel stage, which is the most common reason this jam turns out runny.
Funnel the finished jam into prepared jars, leaving 1/4 inch headspace. Remove air bubbles, wipe the rims, and apply two-part canning lids.
For immediate use, store in the refrigerator. For shelf-stable jars, process in a water bath canner for 10 minutes (10 minutes below 6,000 feet, 15 minutes above). Let the jars rest in the canner 5 minutes, then cool and check the seals after 24 hours.
Notes
Yield: This recipe makes about 2 half-pint jars. The jam thickens as it cools, so it will look looser in the pot than in the finished jar. Two cups of sliced kumquats is about 3/4 pound by weight.Reaching Gel Stage: After adding the sugar, bring the jam to a full rolling boil. A gentle simmer tops out near the boiling point of water and will not reach gel stage at 220 degrees F. This is the most common reason kumquat jam turns out runny.Doubling: Don't double this recipe. Larger batches take much longer to cook down and often fail to set. Make single batches back to back instead.Low Sugar Kumquat Jam: Use 1/2 cup of sugar instead of the full cup for a tarter jam. It still gels from the seed pectin, with a slightly lower yield. For no sugar at all, use a low-sugar pectin like Pomona's.The Seeds Are the Pectin: Reserve the seeds, tie them in cheesecloth, and cook them in the pot, then remove the packet before jarring. They are the natural pectin source that sets this jam.Cook Uncovered: Keep the lid off the whole time so the extra water can cook away. A covered pot leaves the jam runny.Altitude Adjustment: Process for 10 minutes at elevations below 6,000 feet, or 15 minutes above 6,000 feet.