This research focuses on the challenge of defining the ellipsoidal boundaries of the reachable set (RS) for neutral-type dynamical systems with time delays. A novel analytical approach is proposed, leveraging the development of new Lyapunov functions and matrix inequality techniques. These methods provide powerful tools for determining the ellipsoidal boundaries of the system's RS. A comparative analysis, supported by numerical examples, demonstrates that the approach outlined in this study can accurately identify smaller yet effective RS boundaries compared to existing literature. This precise boundary determination offers significant theoretical support for state estimation and control design in dynamical systems, thereby enhancing their effectiveness and reliability in real-world applications.