Cut off the green outer skin and cut the rind into 1- by 2-inch pieces.
Combine the water and kosher salt in a large pot and bring to a boil. Add the rind pieces and boil until tender, for a total time of about five minutes.
Drain the liquid and reserve it. Put the rinds in a large metal bowl.
Pour the reserved liquid into a saucepan and bring the mixture to a boil over medium high heat and stir until the sugar dissolves. Let it simmer for 15 minutes, until the liquid is slightly reduced.
Pour the liquid into the bowl over the watermelon rinds. Put a plate in the bowl on the top of the rinds to keep them submerged in the liquid. Cover the bowl and refrigerate for at least eight hours, but overnight is better.
The next day, ladle the rinds and liquid into pint jars. Store the jars in the refrigerator for up to 2 weeks.