Combine first 4 ingredients in a bowl, stirring well with a whisk. Add crabmeat; toss gently to coat.
Place one tomato slice on each of 6 plates; sprinkle evenly with 1/8 teaspoon salt and 1/8 teaspoon pepper. Divide crab mixture evenly over tomatoes. Arrange remaining tomato slices over crab mixture; sprinkle evenly with remaining 1/8 teaspoon salt and remaining 1/8 teaspoon pepper. Garnish with tarragon springs, if desired.