Cut up the watermelon into chunks and then put the watermelon and fresh lime juice into a high-powered blender and blend until you have a very smooth puree.
Pour the watermelon juice into six popsicle molds. Leave a ¾ inch gap between the liquid and the lid to allow for expansion. Add the lid to each popsicle mold and then freeze it for 2-3 hours or until fully frozen.
Use a seedless watermelon so you won't find any hard black seed pieces in your popsicles. If you use a watermelon with seeds, try to pick out as many of the seeds as you can. The small white seeds are fine to leave, but the black seeds won't blend very well.
Use fresh lime juice, the stuff in the squeezy bottle does not taste the same.