Bring water and sugar to a simmer, stirring until the sugar is dissolved. Increase heat to boil (you want the mixture to just barely boil--have small bubbles on the surface), reduce heat, and let cook for 5 minutes. Remove from heat. Meanwhile, put herbs in a glass bowl. Now, remove 1/2 cup of the hot syrup from the pan, and pour over the herbs. Cover the bowl, and let stand until cool. let the remaining syrup cool also. (can refrigerate). Pour the herb syrup through a fine sieve, discarding herbs. Puree honeydew melon cubes in a blender, add the remaining cooled sugar syrup plus a pinch of salt. Combine the melon syrup mixture with the herb syrup. Refrigerate until cold, then freeze in an ice cream maker. When frozen, transfer to an airtight container and retain in freezer.