Make the simple syrup: In a small saucepan, combine the sugar and water. Heat over medium, stirring occasionally, until the sugar dissolves completely, about 3-4 minutes. Remove from heat and let cool to room temperature.

While the syrup cools, prepare the watermelon. Cut the watermelon into 1-inch cubes, discarding the rind. Working in batches if needed, blend the watermelon cubes in a blender until completely smooth, about 30-45 seconds.

Place a fine-mesh strainer over a large bowl or pitcher. Pour the blended watermelon through the strainer, using a spatula to press the pulp and extract as much juice as possible. Discard the solids. You should have about 2 cups of watermelon juice.

Juice the limes: Roll each lime on the counter under your palm to loosen the juices. Cut in half and juice with a citrus juicer. Measure 1/2 cup of fresh lime juice.

Assemble the limeade: Add the watermelon juice, lime juice, and cooled simple syrup to the pitcher. Stir well to combine. Taste and adjust: add a little more lime for tang or a splash more simple syrup for sweetness, depending on your preference.

Serve: Fill glasses with ice. Pour the watermelon limeade over the ice. Garnish with a lime slice and a mint sprig if desired. Stir before drinking, as the pulp can settle.