Step 1

Combine sugar and water in a small sauce pan. Heat over medium, swirling the pan occasionally, until the sugar dissolves and the mixture starts to simmer.

Step 2

Remove from heat and add the tarragon, bending or breaking them to fit in the pan. Cover and allow to come to room temperature. Strain into a 1/2 pint jar or other suitable container. Refrigerate. Will keep for about a month.

Step 3

Seed melon half, and cut into slices. Remove the rind, and cut the flesh into chunks. Place chunks in blender, and purée until smooth. Strain through a fine mesh strainer into a 2-cup measure. You should have about 3/4 cup juice.

Step 4

Add rum, lime juice, and simple syrup to the melon juice. Stir to combine thoroughly, then divide between 2 highball glasses. Add several ice cubes, and top each glass with 4-6 ounces of selzer. Garnish with tarragon sprigs if desired.