We use calibrated extreme-UV (EUV) spectral irradiances obtained from observations with the Solar & Heliospheric Observatory (SOHO) Coronal Diagnostics Spectrometer Normal Incidence Spectrometer (NIS) to estimate the signal measured by the Solar EUV Monitor (SEM) first-order band, 260 to 340 A (SEM 1). The NIS observes the resonance lines He ii 304 A and Si xi 303 A directly in second order. The irradiances of the other lines in the band are estimated with a differential emission measure (DEM) modelling, using updated atomic data. The observations analysed here were obtained during 1998–2011, which means that they span the maximum and minimum of Cycle 23. The current knowledge of the SEM 1 degradation is used to find effective areas during the dates of the NIS observations and to predict the SEM 1 count rates across the band. The total count rates, estimated by folding the NIS-based spectra with the SEM 1 effective areas, agree very well (within 10–20%) with the observed ones during solar minimum conditions, when the He ii 304 A is the dominant contribution to the band. Excellent agreement with the Solar Dynamics Observatory (SDO) Extreme ultraviolet Variability Experiment (EVE) observations is also found. On the other hand, the predicted SEM 1 count rates during the Cycle-23 maximum are significantly (by about 30%) lower than the observed ones. The solar spectrum in the SEM 1 band changes significantly during maximum conditions, with the He ii 304 A only contributing about 40%. A significant fraction of the observed count rates comes from coronal emission in an off-band spectral region that has recently been discovered. An explanation for the discrepancy needs further investigation.