In this work, a novel formulation of the Cauchy method is presented, which can be applied in the extraction of circuit models from measured (lossy) response of microwave filters. The presented extrapolating technique is integrated into a novel computer-aided tuning procedure for microwave filters exploited in base stations for mobile communications. This procedure uses also a synthesis technique analytically performed (no optimization required). The suitable combination of these techniques furnish a very fast algorithm which can be adopted for a real-time tuning process. Experimental examples on different base-station filters employed in GSM and UMTS communication systems has confirmed its effectiveness. The duplexer modeling using the Cauchy method has also been considered. This work presents innovative, accurate, and robust formulations and make the Cauchy method suitable for the extraction of a high order microwave duplexer polynomial model.