Bring a medium pot of water to a boil. Plunge the fresh tomatoes into the boiling water, and simmer for 30 seconds. Remove the tomatoes from the boiling water, and cool briefly. Gently peel away the loosened skin, and remove the tomato core. Chop finely and set aside.
Add half of the chopped tomatoes to a medium-sized microwavable bowl. Add the kumquats, sugar, minced jalapeño, lemon zest and orange zest. Cover with the remaining half of the tomatoes, and add the lemon juice. Place the bowl in the microwave, and cook uncovered on high for 5 minutes.
Remove from the microwave, and stir once or twice. Return the bowl to the microwave and cook on high for another 10 minutes, pausing to stir every 3 minutes. Remove the bowl from the microwave, and allow to cool completely before serving.