The paper proposes a novel method for the optimal parameter selection of the discrete-time switch model used in circuit solvers that adopt the Fixed Admittance Matrix Nodal Method (FAMNM) approach. As known, FAMNM-based circuit solvers allow to reach efficient computation times since they do not need the inversion of the circuit nodal admittance matrix. However, these solvers need to optimally tune the so-called discrete switch conductance, since this parameter might largely affect the simulations accuracy. Within this context, the method proposed in the paper minimizes the distance between the eigenvalues of the original circuit’s nodal admittance matrix with those associated with the presence of the discrete-time switches. The method is proven to provide values of the discrete-time switch conductance that maximize the simulation accuracy and minimize the losses on this artificial parameter. The performances of the proposed method are finally validated by making reference to two test cases: (i) a circuit composed of RLC elements, (ii) a network model that includes a single-phase transmission line.