Use a sharp chef's knife and cutting board to peel the green rind from the watermelon, removing as much white pith as possible, then chop the rind into small, uniform pieces.
Transfer the chopped rind to a large saucepan and add 2 cups of water and 1/2 teaspoon of salt. Bring the mixture to a gentle simmer over medium heat, listening for a soft bubbling sound.
Allow the mixture to simmer on low heat for about 15-20 minutes, or until the rind becomes translucent and aromatic. The water should turn slightly cloudy and emit a grassy fragrance.
Remove the saucepan from heat and let the mixture cool slightly for 5 minutes. Strain the liquid through a fine mesh strainer into a bowl, pressing gently to extract as much flavor as possible, leaving behind the softened rind pieces.
Pour the strained watermelon rind water into glasses and serve chilled. No pulp is present, and the liquid appears clear with a faint greenish tint, ready to enjoy as a fresh, aromatic water.