In a food processor, combine the tomatoes, olive oil, red wine vinegar, thyme, tarragon, garlic, sherry vinegar and cayenne and process until smooth. Season lightly with salt and black pepper. Transfer the puree to a bowl and refrigerate for at least 1 hour and up to 1 day.
Just before serving, strain the tomato juice through a fine sieve, pressing on the tomatoes. Season again with salt and pepper. Whisk until frothy, then pour into small cups and serve.