Wash the kumquats in warm water; drain and dry. Gently prick each kumquat with a skewer in 2 or 3 places.
Combine the water and sugar in a saucepan (not aluminum). Bring to a boil and the kumquats. Cook over low heat 20 minutes, or until syrup is thick and clear. Stir in the ginger and lime juice. Pack in sterile jars and seal. Makes about 3 pints.