In a blender, purée chilled honeydew chunks, half at a time, with 2/3 cup water. Strain.
In a bowl, combine purée, 1/4 cup sugar, 1/4 cup lemon juice, and the orange-flower water. Add more sugar and lemon juice to taste.
Fill 8 glasses with ice and add equal parts melon purée and sparkling water; stir. Crush mint sprigs in your hands and add to drinks.
*Find with cocktail supplies.
Make ahead: Up to 2 days, chilled.