In a food processor or blender, pulse the celery, shallot, and garlic, until finely chopped. Alternatively, you can do this by hand.
Add the celery mixture along with the tomatoes, cilantro, and salt to a large, non-reactive saucepan and set it over medium-high heat. Bring to a simmer, then cover, turn the heat to low, and cook until the tomatoes have begun releasing their juices, about 20 minutes.
Crush the tomatoes with a potato masher, fork, or ladle to break them apart. Cook for another 20 minutes, until very soft and soupy.
Strain the mixture through a fine mesh sieve or food mill.
Stir in the lime juice and siracha. Taste for seasoning.
Chill in the refrigerator in an airtight container until ready to use.
To serve, dust the tops of 4 glasses with a little salt. Add 1/4 cup of tequila, followed by 1 cup of the spicy tomato juice, and stir to combine. Garnish with celery sticks, lemon slivers, and plenty of herbs.