Abstract: We report measurements of the energy resolution of ultrasensitive superconducting bolometric detectors. The device is a superconducting titanium nanobridge with niobium contacts. A fast microwave pulse is used to simulate a single higher-frequency photon, where the absorbed energy of the pulse is equal to the photon energy. This technique allows precise calibration of the input coupling and avoids problems with unwanted background photons. Present devices have an intrinsic full-width at half-maximum energy resolution of approximately 23 THz, near the predicted value due to intrinsic thermal fluctuation noise.