Roughly chop the leftover watermelon flesh into small chunks and place them into the blender.
Add lime juice and a pinch of salt to the blender.
Blend on high speed until the mixture is smooth and slightly frothy, about 30 seconds, with no large chunks remaining.
Place a fine-mesh sieve or strainer over a large bowl and pour the blended mixture through it, using a spoon or spatula to press the pulp and extract as much liquid as possible.
Discard the pulp residue and transfer the strained juice into glasses. Chill in the refrigerator for at least 10 minutes before serving.
Serve the juice cold, optionally garnished with a lime wedge or a sprinkle of salt on top.