The Engine Control Module (ECM) in a 2001 Cadillac Catera is located
under the hood, usually near the firewall on the passenger side. However, the exact location can vary slightly depending on options and specific vehicle build. It's often attached to the inner fender well or secured to a bracket nearby. It's a fairly large, rectangular electronic unit.
To be certain, you should consult a repair manual specific to your 2001 Cadillac Catera. A Haynes or Chilton manual would show a detailed diagram and location. You can also find diagrams online, but be very careful to ensure the diagram matches your specific year and model.