For computer-aided tuning of narrowband coupled resonator networks, coupling matrices can be extracted from measured or simulated data based on rational function approximation techniques. In the general framework, phase de-embedding is first performed to remove frequency-dependent loading phases produced by feed lines and high-order modes. Then, the phase-corrected data are approximated, and a coupling matrix is constructed using various approaches. After investigating several possible techniques, this article proposes approximating the Y-parameter data using appropriate basis functions and weighting schemes during the rational fitting process. Then, a coupling matrix is directly constructed from the resulting Y-parameter approximation. This approach demonstrates superior robustness in the computer-aided tuning of a wide variety of coupled-resonator networks.