Preheat oven to 400° F. Bring small pot of water to boil. Add celery and carrots; cook 1 minute. Remove, and place in bowl under cold running water. Place on paper towel to dry.
Cut 2 large sheets of baking parchment into 20×20-inch squares; fold in half and lightly crease. Unfold parchment; lightly brush one side of each sheet with olive oil. Divide celery, carrots and onion evenly into small piles on one half of each sheet. Place one fillet on top of each. Lightly fold up edges of parchment to create a small, bowl-like vessel.
Combine wine, lemon juice and clam juice in a bowl. Drizzle each fillet with 3 tablespoons of mixture, ensuring that it is contained in parchment. Place half of the chopped tomato over each fillet and sprinkle half of each fresh herb over tomatoes. Season with salt and pepper.
Fold parchment over fillet and vegetables. Beginning at the creased corner, start folding edges over by ½ inch. Continue until parchment is a series of tight, overlapping folds.
Place papillotes on large baking sheet. Bake 11 minutes or until bags are nicely puffed and slightly browned.