The focus of this thesis is on developing theories and techniques to extract lossy microwave filter parameters from data. In the literature, the Cauchy methods have been used to extract filters’ characteristic polynomials from measured scattering parameters. These methods are described and some examples are constructed to test their performance. The results suggest that the Cauchy method does not work well when the Q factors representing the loss of filters are not even. Based on some prototype filters and the relationship between Q factors and the loss, we conduct preliminary studies on alternative representations of the characteristic polynomials. The parameters in these new models are extracted using the Levenberg–Marquardt algorithm to accurately estimate characteristic polynomials and the loss information.