In a 1- to 1 1/2-quart pan, combine vinegar, honey, 1/4 cup water, mustard seeds, celery seeds, and salt. Simmer over medium heat for 5 minutes, then boil over high heat, stirring often, until reduced to 1/2 cup, about 2 minutes longer. Let cool.
In a salad bowl, combine vinegar mixture, honeydew, cucumber, diced celery, and grapes. Cover and chill, stirring occasionally to blend flavors, at least 15 minutes and up to 1 hour.
Stir in celery leaves and chives. If using butter lettuce leaves, arrange on plates and spoon salad over them.
Note: Nutritional analysis is per serving.