- In a blender, purée the melon cubes until smooth. Strain through a fine sieve, without pushing down on the pulp, to extract only the juice (see note). Compost the pulp.
- Place the ice cubes in a spritzer glass. Add the Lillet, melon juice and tonic. Thread the melon balls onto a toothpick. Place in the glass along with the lemon balm sprig, if desired.
Depending on the size of your honeydew, you may have enough juice to make several cocktails.