This paper presents a computation method of generalized scattering matrix (GSM) based on integral equations and the method of moments (MoM), specifically designed for antennas excited through waveguide ports. By leveraging two distinct formulations -- magnetic-type and electric-type integral equations -- we establish concise algebraic relations linking the GSM directly to the impedance matrices obtained from MoM. To address practical challenges in storing GSM data across wide frequency bands and multiple antenna scenarios, we propose a efficient compression scheme. This approach alleviates memory demands by selectively storing the dominant eigencomponents that govern scattering behavior. Numerical validation examples confirm the accuracy of our method by comparisons with full-wave simulation results. Furthermore, we introduce an efficient iterative procedure to predict antenna array performance, highlighting remarkable improvements in computational speed compared to conventional numerical methods. These results collectively demonstrate the GSM framework's strong potential for antenna-array design processes.