Melt butter in a large saucepan over medium heat. Stir in onion, celery, bell pepper, garlic, cayenne pepper and black pepper. Cook and stir until vegetables are tender.
Stir in flour to make a roux. Cook and stir for 2 minutes.
Gradually stir in chicken broth and tomatoes with juice. Bring to a boil; reduce heat to low and simmer for 10 minutes.
Stir in crawfish tails; cook until heated through.