This paper introduces SyMPVL, an algorithm for the approximation of the symmetric multi-port transfer function of an RLC circuit. The algorithm employs a symmetric block-Lanczos algorithm to reduce the original circuit matrices to a pair of typically much smaller, banded, symmetric matrices. These matrices determine a matrix-Pade approximation of the multi-port transfer function, and can serve as a reduced-order model of the original circuit. They can be ``stamped'' directly into the Jacobian matrix of a SPICE-type circuit simulator, or can be used to synthesize an equivalent smaller circuit. We also prove stability and passivity of the reduced-order models in the RL, RC, and LC special cases, and report numerical results for SyMPVL applied to example circuits.