Accurate prediction of spin-wave modes in magnetic thin films is essential for the design of spintronic and magnonic devices. In this work, we present a highly efficient method for determining both the dispersion relations and mode profiles of spin waves (SWs) in magnetic thin films while simultaneously accounting for exchange and dipolar interactions, uniaxial magnetic anisotropy, Gilbert damping, electrical conductivity (relevant for metallic films such as FeCoB), and an external magnetic field applied in an arbitrary direction. The method is based on the coupled solution of the Landau–Lifshitz–Gilbert equation and Maxwell’s equations in a conducting medium under the appropriate electromagnetic and magnetic boundary conditions. By expanding both the dynamic magnetization and the magnetic field onto a basis of Legendre polynomials, the coupled equations are transformed into an eigenvalue problem whose eigenvalues and eigenvectors directly provide the spin-wave dispersion relations and mode profiles, respectively. The method is validated through comparison with previously published results, showing excellent agreement. For insulating films, the calculated complex dispersion relations reveal the existence of evanescent modes below the cutoff frequency. In conducting films, the influence of electrical conductivity becomes significant at low wavevectors, particularly in the vicinity of the cutoff frequencies, where backward-volume SWs exhibit strong attenuation. The method is then applied to investigate the evolution of spin-wave modes in anisotropic conducting magnetic films near a spin-reorientation transition (SRT) induced by an external magnetic field applied perpendicular to the easy axis. We show that the character of the propagating modes depends strongly on the applied field. As the field increases from zero to values exceeding the anisotropy field, the modes evolve from backward-volume (BV) waves to Damon–Eshbach (DE) surface waves. Furthermore, in the vicinity of the SRT, strong mode hybridization is observed, both between surface and volume modes and among volume modes themselves.