The limits of detection (LOD) and quantitation (LOQ) in the mass domain, for broadband vibrational spectroscopy with neutrons on the TOSCA spectrometer at the ISIS Pulsed Neutron and Muon Source (UK), have been studied. The well-known 3σ and 10σ approaches are used through a specifically developed analytical procedure that is based on the calculation of the integrated spectral intensities in selected energy-transfer ranges, as a function of mass of standard reference materials and calibrants, such as ZrH2, 2,5-diiodothiophene, and low-density polyethylene. The analysis shows that the blank, that is, the instrument setup without the analyte, plays a critical role in the measurement performance, especially for small specimen quantities. The results point that TOSCA enables detection of 128 μmol (LODH) and quantitation of 428 μmol (LOQH) of elemental hydrogen analytes in ZrH2. The determined values for this and other standards allow for the assessment of the calibration curve design and instrument sensitivity and define a method to be used for inelastic neutron scattering spectrometers such as TOSCA, or VESPA, the new beamline under construction at the European Spallation Source in Lund (Sweden).