Add chopped watermelon to a blender and purée until smooth.
Line a fine mesh sieve with a strip of folded cheesecloth or a jelly strainer bag. Pour the puréed watermelon through the sieve into a large bowl or measuring cup with lip.
Measure out 4 cups of of watermelon juice. Reserve leftover juice (if any) to enjoy later as a beverage.
Transfer watermelon juice to a saucepan and bring to a boil along with the lime juice and boxed pectin (do NOT add sugar yet). Whisk to dissolve.
Boil the juice and pectin for 1 minute.
After 1 minute, whisk in the sugar to dissolve. Boil for 1 more minute.
Carefully ladle the watermelon and lime juice, pectin, and sugar mixture into prepared jars, leaving 1/4-inch headspace.
Wipe down the rims and sides of each jar with a clean kitchen towel. Apply two-piece lids until fingertip tight.
At this point, the jelly can be transferred to the refrigerator—enjoy within 3 weeks. The jelly will take 12-24 hours to set.
To can this watermelon jelly: process jars in a hot water canner for 10 minutes (or 15 minutes if above 6,000 feet in elevation). Using a jar lifter, transfer jars from canner to a clean kitchen towel, leaving 1-inch of space between each jar. Let the jelly to come to room temperature before inspecting the seal of each jar—any unsealed jars should be transferred to the refrigerator. Sealed jars should be stored in a cool, dry place away from direct sunlight for up to 18 months.