This paper describes a new method for analyzing the high-frequency EM scattering from large open-ended cavities. Iterative solutions based on Physical Optics (PO), such as the Iterative Physical Optics (IPO) or the Progressive Physical Optics (PPO) method, have proved to be efficient techniques for computing the scattering of relatively shallow cavities. In order to improve the efficiency for deep cavities a segmented approach is proposed. In this technique the cavity is split into several sections and the magnetic field integral equation (MFIE) is solved independently for each of them, using either IPO or PPO to obtain their scattering matrices. The response of the whole cavity is found via a connection algorithm which leads to evaluate a generalized reciprocity integral over a surface close to the cavity end. This approach reduces drastically the computational cost with respect to both IPO and PPO methods, mainly for deep cavities. Some numerical results are compared with a modal reference solution to demonstrate the accuracy and efficiency of the new approach.