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This paper describes a new algorithm for obtaining time-domain sensitivity information of large linear networks via projection-based model-order reduction (MOR) techniques. The proposed algorithm enables adjoint-based time-domain sensitivity analysis techniques to be applied to a large network containing multiple linear multiport subnetworks. In addition, the proposed algorithm can also be used to obtain frequency-domain sensitivity information. The efficiency and accuracy of the proposed work is demonstrated through optimizing the time-domain waveforms of a high-speed interconnect circuit with nonlinear terminations.