Drain crab meat on several layers of paper towels. Thinly slice tops and bottoms from tomatoes. With a small melon ball cutter, remove pulp and drain upside-down on paper towels.
In a small bowl, mix crab meat, mayonnaise, parsley, mustard and salt until well blended; stuff tomatoes. Chill at least 30 minutes.
Serve on a tray garnished with parsley or watercress.