1. Place first 4 ingredients in a blender; process until smooth. Remove center piece of blender lid; secure blender lid on blender. With blender on, drop melon cubes, 1 to 2 at a time, through lid. Process until smooth.
2. Fill 4 glasses with ice. Pour 3/4 cup honeydew mixture over ice in each glass; add 1/3 cup club soda to each glass. Garnish with lime slices, if desired.