Slice off and dispose of rough stems from celery hearts; keep stalks attached to bases; cut off and dispose of tops so stalks are 8 inches long. Wash and dry celery hearts. Using a vegetable peeler, peel coarse strings from outer stalk backs. Slice each heart in half lengthwise; secure each half tightly around middle with cotton string.
Mix celery and broth in a 5- to 6-quart pan (at least 10 inches wide). Let boil over high heat. Place lid on pot, lower heat, and simmer until celery is fork tender, 12 to 15 minutes, flip bundles when about halfway cooked.
Mix together olive oil and vinegar in a 1-gallon heavy resealable plastic bag. Using tongs, move celery from broth to bag. Set upright and let cool to room temperature.
In the meantime, place shrimp in broth and let simmer over high heat; lower heat and simmer, just until shrimp are opaque but still moist-looking in center, 30 seconds to 1 minute. Using a slotted spoon, take shrimp out of broth and move to plastic bag with celery (reserve broth for other uses or dispose of). Let cool, about 30 minutes, then close bag. Shake bag to coat celery and shrimp with dressing. Refrigerate until cold, at least 2 hours or up to 1 day, flipping bag occasionally.
Take celery out of dressing; remove and discard strings, and arrange a bundle on each dinner plate. Using a slotted spoon, move shrimp from dressing and lay beside celery.
Crisscross 2 anchovy fillets on each portion, then top with capers. Arrange watercress around celery and shrimp. Drizzle the rest of the dressing from the bag over salads, and season salt and pepper.