Cut the peeled limes in half and squeeze the juice. Set the juice aside.
Scrape the pulp and seeds from the lime halves. Place in a cheesecloth bag. Place the cheesecloth bag, zest, juice, and water in a 6-quart saucepan, then cover them and soak overnight, or for about 8 hours.
Bring the water mixture to a boil and cook about 2 hours, until the peels are soft. Remove the cheesecloth bag. Add the sugar to the pan and stir to dissolve. Boil, stirring often, until a cooking thermometer reaches 220 degrees F.
Ladle into clean jars, leaving 1/4 inch of headspace. Cap and seal. Process for 10 minutes in a boiling-water-bath canner. Adjust for altitude, if necessary.
Yield: 10 pints