Trim and discard tough stem ends from celery hearts, keeping stalks attached to bases; trim and discard tops to make stalks about 8 inches long. Rinse and drain celery hearts. With a vegetable peeler, pare coarse strings from outer stalk backs. Cut each heart in half lengthwise; tie each half tightly around center with cotton string.
Combine celery and broth in a 5- to 6-quart pan (at least 10 in. wide). Bring to a boil over high heat; cover, reduce heat, and simmer until celery is tender when pierced, 12 to 15 minutes, turning bundles over halfway through cooking.
Combine olive oil and vinegar in a 1-gallon heavy plastic food bag. With tongs, transfer celery from broth to bag. Set upright and let cool.
Meanwhile, add shrimp to broth; bring to a simmer over high heat, then reduce heat and simmer, uncovered, just until shrimp are opaque but still moist-looking in center of thickest part (cut to test), 30 seconds to 1 minute. With a slotted spoon, lift shrimp from broth and add to plastic bag with celery (save broth for other uses or discard). Let cool, about 30 minutes, then press bag to seal. Turn bag to coat celery and shrimp with dressing. Chill until cold, at least 2 hours or up to 1 day, turning bag occasionally.
Lift celery from dressing; remove and discard strings, and place a bundle on each dinner plate. With a slotted spoon, lift shrimp from dressing and mound beside celery.
Crisscross 2 anchovy fillets on each portion, then sprinkle with capers. Tuck watercress around celery and shrimp. Spoon remaining dressing from bag over salads, and add salt and pepper to taste.