1. Using a melon baller, scoop 1-inch balls from melons and combine in a bowl. Fold in mint and zest. Refrigerate.
2. Bring sugar, 1/3 cup water and ginger to a boil in a pan over medium-high heat, stirring until sugar dissolves. Boil until reduced by half and syrupy, about 6 minutes. Remove from heat; stir in juice. Pour into a container and refrigerate until chilled.
3. When ready to serve, spoon melon balls into 4 bowls. Strain syrup and spoon 1 Tbsp. over each bowl. Garnish with more mint, if desired.