Magnon-photon coupling in planar cavities provides a promising platform for integrated cavity magnonics devices. However, its characterization becomes challenging in ultrathin magnetic films because their weak magnetic response can be obscured by the much stronger microwave background. Here, we employ the derivative-divide method to extract the field-dependent magnetic response from transmission measurements of split-ring resonators. The method reveals clear magn-photon anticrossings that are hardly discernible in conventional transmission spectra and enables quantitative extraction of the coupling strength. We resolve coupling in yttrium iron garnet films down to 60 nm and extend the approach to conductive CoFeB films down to 5 nm. Our results demonstrate a practical method for characterizing magno-photon coupling in ultrathin magnetic films, providing an experimental route toward cavity magnonics systems based on ultrathin magnetic films.