Combine kumquats, 3 cups water and lemon juice in a large Dutch oven; bring to a boil. Reduce heat and simmer, uncovered, for 20 minutes, stirring often. Add remaining 1/2 cup water. Stir in pectin; bring to a boil, stirring constantly. Stir in sugar; bring to a boil. Boil 4 minutes, stirring constantly. Remove from heat; skim foam off top of mixture and discard.