After squeezing, wrap segments and seeds from the mesh strainers in cheesecloth. Slice kumquat rinds into thin strips. Combine cheesecloth bundle, rinds, and kumquat juice all into the same bowl, and add the 3 cups of water. Cover and set aside in refrigerator for at least 12 hours to help soften the kumquat rinds.
Put all of previous day's contents (liquid, rinds, and cheesecloth bundle) into a medium saucepan. Stir in the sugar.
Bring contents up to a boil. Reduce heat to medium and boil for about 45 minutes, but it may take longer depending on your heat, pan, and quantity of kumquats. Stir occasionally to prevent the marmalade from burning.
When finished cooking, skim off any surface foam. Let the kumquat marmalade rest for 10 minutes. Pour marmalade into one jar. Wait for a moment to see if rinds float to the top. If so, let marmalade rest for another 5 minutes. If not, then pour kumquat marmalade into the rest of the jars and process according to manufacturer’s instructions.