Superlenses create sub-diffraction-limit images by reconstructing the evanescent fields arising from an object. We study the lateral, vertical, and spectral field distribution of three different perovskite-based superlenses by means of scattering-type near-field microscopy. Sub-diffraction-limit resolution is observed for all samples with an image contrast depending on losses such as scattering and absorption. For the three lenses superlensing is observed at slightly different frequencies resulting in an overall broad frequency range of 3.6 THz around 20 THz.