Cut the honeydew melon into small cubes.
Add melon cubes, mint leaves, lime juice, and simple syrup to the blender.
Blend until smooth, about 30-45 seconds.
Strain the mixture through a fine-mesh strainer into a container.
Fill tall glasses with ice cubes.
Pour the strained melon mixture into each glass, filling about 1/3 full.
Top with sparkling water and stir gently.
Garnish with fresh mint leaves and small honeydew balls.