In a large, stainless steel stockpot, squash the berries just to break them up. You can use a potato masher in the pan to help with the task. Add 2 cups of the water and the lime zest and bring to a boil over medium-high heat, stirring often. Boil the mixture for 5 minutes then remove from the heat.
Line a colander or sieve with two or three layers of cheesecloth and position it over a deep bowl. If you have a super-fine cheesecloth like butter muslin, one layer will suffice. Scoop the boiled blueberry mixture into the cheesecloth and let it drain, undisturbed, for 2 hours. Lay a plate with a little weight on it on top of the blueberry mixture at that point and let it drip for another 15 minutes. Do not squeeze the cheesecloth with your hands, though. You just want juice, not pulp!
Wash out your stock pot to be prepared for the next step.
Stir together the remaining water and the sugar in the clean stockpot and bring to a boil over high heat, stirring just until the sugar is dissolved. Boil it until the mixture reaches 230°F. (**See Notes! Do not skip using a thermometer!) When it reaches 230°F, stir in the blueberry juice and return to a boil. Boil for 5 minutes, remove from the heat, and stir in the lime juice. Ladle the hot syrup into sterilized, prepared pint jars with new two-piece lids, leaving 1/4-inch of headspace. Wipe the rims with a cloth dipped in vinegar, fix the lids in place to finger-tip tight, and place in a canner so that the jars are covered with water. Bring to a boil and process them for 10 minutes. When the 10 minutes is up, shut off the heat, remove the lid from the canner, and let the jars rest in the water for 5 minutes before transferring to a cooling rack or a towel lined counter. Cool completely, wipe clean, label and store in a cool, dark place for up to a year.
Once opened, a jar is good for about 3 weeks.