Add the watermelon to your blender and puree (you might need to do this in batches). Strain the pureed watermelon through a fine-mesh strainer into a large measuring cup (press on the solids to extract as much liquid as possible. Repeat with the strawberries, straining if the seeds bother you. Add the sugar and lime juice to the measuring cup and whisk to dissolve the sugar completely.

Pour into your popsicle molds. Freeze for 30 minutes, then insert the popsicle sticks. Freeze completely then serve.