Cut tomatoes in half crosswise (not through stem end), squeeze out seeds, and chop into about 1/4-inch dice.
In a medium microwave-safe bowl, stir together tomatoes, onion, celery, garlic, vinegars, sugar, pepper, Worcestershire sauce, lemon juice, tomato paste, and salt. Cover with lid or vented plastic wrap and microwave for 30 to 40 minutes or until very thick, stirring every 10 minutes.
Stir in horseradish.
Refrigerate for at least 30 minutes for flavors to blend.
The sauce may be refrigerated up to 2 weeks. Serve with crab cakes, shrimp, or other seafood. Makes 2 1/4 cups.