High-resolution, gamma- and X-ray spectrometry are used routinely in nuclear materials safeguards verification measurements. These measurements are mostly performed with high-purity germanium (HPGe) detectors, which require cooling at liquid-nitrogen temperatures, thus limiting their utility in field and unattended safeguards measurement applications. Sodium iodide (NaI) scintillation detectors do not require cooling, but their energy resolution (10% at 122 keV) is insufficient for many verification measurements. Semiconductor detectors that operate at room temperatures, such as cadmium-zinc-telluride (CZT) detectors, with energy resolution performance reaching 2.0% at 122 keV may be used for certain safeguards verification applications. We have developed hardware to utilize CZT detectors in X- and gamma-ray measurement systems and software to apply such a system in measuring U-235 enrichment for safeguards verification purposes. The paper reports an the CZT detector-based measurement system and measurement results obtained with it The paper also discusses work on additional improvements to broaden the applications of the system.