Chop the celery into 1/4-inch dice, finely dice the red onion, and finely chop the fresh dill and parsley. Having all your vegetables and herbs prepped and ready will make assembly quick and seamless. Set these aside in separate small bowls.
Thaw the shrimp if frozen, then rinse them under cold water and remove the tails. Pat the shrimp dry with paper towels—this is important because excess moisture will dilute your dressing. Cut the shrimp into 1/2-inch pieces and place in a large mixing bowl.
In a small bowl, whisk together the mayonnaise, Old Bay seasoning, Dijon mustard, lemon juice, and hot sauce. I find that whisking the dressing separately before combining ensures even distribution of the seasonings throughout the salad—you won't end up with pockets of under- or over-seasoned shrimp. Taste and adjust the seasoning as needed.
Pour the dressing from Step 3 over the shrimp, then add the chopped vegetables and herbs from Step 1 (celery, red onion, dill, and parsley). Fold everything together gently with a spatula or large spoon until evenly coated. Season to taste with salt and freshly cracked black pepper. I like to let the salad sit for 5-10 minutes before serving so the flavors have time to meld together.
Tear the chilled romaine lettuce into 2-inch pieces and arrange on a serving plate or platter. Spoon the shrimp salad from Step 4 generously over the lettuce. Serve immediately while everything is cold and crisp.