Kaonic atom X-ray spectroscopy is a consolidated technique for investigations on the physics of strong kaon–nucleus/nucleon interaction. Several experiments have been conducted regarding the measurement of soft X-ray emission (<20 keV) from light kaonic atoms (hydrogen, deuterium, and helium). Currently, there have been new research activities within the framework of the SIDDHARTA-2 experiment and EXCALIBUR proposal focusing on performing precise and accurate measurements of hard X-rays (>20 keV) from intermediate kaonic atoms (carbon, aluminum, and sulfur). In this context, we investigated cadmium–zinc–telluride (CdZnTe or CZT) detectors, which have recently demonstrated high-resolution capabilities for hard X-ray and gamma-ray detection. A demonstrator prototype based on a new cadmium–zinc–telluride quasi-hemispherical detector and custom digital pulse processing electronics was developed. The detector covered a detection area of 1 cm2 with a single readout channel and interesting room-temperature performance with energy resolution of 4.4% (2.6 keV), 3% (3.7 keV), and 1.4% (9.3 keV) FWHM at 59.5, 122.1, and 662 keV, respectively. The results from X-ray measurements at the DAΦNE collider at the INFN National Laboratories of Frascati (Italy) are also presented with particular attention to the effects and rejection of electromagnetic and hadronic background.