1. Combine sugar and 1/2 cup water in a small saucepan, and simmer over medium heat, stirring constantly, until sugar dissolves. Set aside to cool.
2. Puree watermelon, strawberry, and lime juice in a food processor until smooth. Strain through a fine mesh strainer, pressing lightly, and discard solids.
3. Combine watermelon puree with kosher salt and reserved syrup. Chill thoroughly, and serve over ice in cold glasses.