To achieve efficient multi-port model order reduction, a multi-port Cauer ladder network (CLN) method is formulated that directly yields resistance and inductance matrices that constitute the network elements in the matrix Cauer form. The eddy-current field driven by multiple power sources is accurately reconstructed using a small number of network elements. The matrix Cauer form achieves faster convergence of the transfer function than a single-port CLN method and almost the same convergence as a block Pade via Lanczos (PVL) method.