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To overcome the limitations of traditional interconnects, transmission lines that transmit multi-channel signals via high frequency carriers have recently been proposed and realized for intra-chip and inter-chip communication. We derive a closed-form model for SNR for such interconnects with multiple ports and branches, and propose efficient figures of merit (FOMs) to minimize signal distortion. Experiments show that the SNR model is accurate compared to SPICE simulation and signal distortion FOMs are effective. Using the proposed models, we further automatically synthesize coplanar waveguides for radio-frequency (RF) interconnects with capacitive couplers. We minimize the total interconnect area under constraints of SNR and signal distortion. Compared to the published manual designs, the synthesized solution can reduce up to 80% area. Furthermore, the optimized solutions vary greatly with respect to number of ports, frequency bands, topologies and terminations, and therefore automatic synthesis is needed.