<p>In the duplexer filtering of the three-port network microwave application, three coupled rational functions need to be reconstructed by fitting sampled responses measured at a set of frequencies efficiently and effectively. Traditionally, the Cauchy method and its modifications are common approaches that find the underlying rational functions by solving the linearized system. However, with increasing degrees of polynomials, Cauchy methods encounter difficulties when applied to modern duplexer hardware, particularly due to the ill-conditioned Vandermonde matrices involved and a large variation of order of magnitude (dB) in the noise-contaminated and lossy responses. In this paper, by relying on recent achievements from the rational approximation literature using barycentric representations, namely the “adaptive Antoulas-Anderson” (AAA) algorithm and Lawson’s iteration for scalar-valued as well as matrix-valued functions, we propose a vector-valued AAA-type approach (<Emphasis FontCategory="NonProportional">v-AAA-Lawson</Emphasis>) for addressing the duplexer filtering problem, which is also applicable for the general matrix-valued rational approximations. Numerical experiments demonstrate that the new method is able to improve significantly the performance of the Cauchy methods both in accuracy and robustness.</p>