The finite-difference time-domain (FDTD) method and the transmission line matrix (TLM) method allow the formulation of state-equation representations of the discretized electromagnetic field. These representations usually involve very large numbers of state variables. Reduced order modeling (ROM) of the investigated structure may yield considerable reduction of the computational effort and can be used to generate compact models of the electromagnetic system. While complexity reduction approaches based on moment matching techniques have been intensively studied in the case of FDTD, they have not yet been considered for TLM. In this paper we apply Krylov subspace methods to TLM using the basic Arnoldi and non-symmetric Lanczos algorithm. It is shown that the inherent unitarity property of the TLM operator nevertheless implies an essential difference in comparison to former implementations for FDTD or circuit analysis. Simulation results for a rectangular cavity resonator using both TLM with and without ROM and a study of the convergence of the eigenvalues are presented here. Index Terms-Transmission Line Matrix (TLM) Method, Reduced Order Modeling (ROM).