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This paper presents a new method for obtaining the congruence transformation matrix for model order reduction of linear interconnect systems with large numbers of constrained ports. Model order reduction techniques have proven to be very effective for the simulation of large interconnect networks. However, using current model order reduction techniques, the size of the reduced system grows rapidly as the number of ports increases. This leads to a severe reduction in efficiency. In this paper, a new method is proposed, which is based on imposing practical restrictions on the loads that can be connected to the ports of the network. Specifically, constrained ports terminated by combined resistive and capacitive loads are considered. The reduction matrix is then computed while exploiting the information on the constrained ports and utilizing parametric model order reduction techniques, the resulting reduced model is significantly smaller than standard reduced models. Examples are presented that demonstrate the accuracy and efficiency of the new method.