Cover eggs with cold water by 1½ inches in a 4- to 5-quart pot and bring to a rolling boil, partially covered with lid. Reduce heat to low and cook eggs, covered completely, 30 seconds. Remove pot from heat and let eggs stand in hot water, covered with lid, 15 minutes. Rinse eggs under cold water 5 minutes to stop cooking.
Peel eggs and halve lengthwise. Carefully remove yolks and mash in a bowl with a fork. Add mayonnaise, mustard, pickles, celery, and salt and pepper to taste to yolks and stir with fork until combined well, then spoon into egg whites.