We have identified a sample of 33 Sun-like stars observed by the International Ultraviolet Explorer(IUE) with the short-wavelength spectrographs that have ground-based detections of chromospheric Ca ii H+K activity. Our objective is to determine if these observations can provide an estimate of the decrease in ultraviolet (UV) surface flux associated with a transition from a normal stellar cycle to a grand-minimum state. The activity detections, corrected to solar metallicity, span the range , and eight stars have log . The IUE-observed flux spectra are integrated over the wavelength range 1250–1910 Å, transformed to surface fluxes, and then normalized to solar B − V. These normalized surface fluxes show a strong linear relationship with activity (R2 = 0.857 after three outliers are omitted). From this linear regression we estimate a range in UV flux of 9.3% over solar cycle 22 and a reduction of 6.9% below solar cycle minimum under a grand minimum. The 95% confidence interval in this grand-minimum estimate is 5.5%–8.4%. An alternative estimate is provided by the IUE observations of τCet (HD 10700), a star having strong evidence of being in a grand-minimum state, and this star's normalized surface flux is 23.0 ± 5.7% lower than solar cycle minimum.