We present optical vector network analysis (OVNA) of an isotopically purified Er1663+:LiYF47 crystal. The OVNA method is based on generation and detection of a modulated optical sideband by using a radio-frequency vector network analyzer. This technique is widely used in the field of microwave photonics for the characterization of optical responses of optical devices such as filters and high-Q resonators. However, dense solid-state atomic ensembles induce a large phase shift on one of the optical sidebands that results in the appearance of extra features on the measured transmission response. We present a simple theoretical model that accurately describes the observed spectra and helps to reconstruct the absorption profile of a solid-state atomic ensemble as well as corresponding change of the refractive index in the vicinity of atomic resonances.