The physical conditions in the narrow-line regions of two Seyfert 2 galaxies, NGC 7674 and I Zw 92, are examined using IUE spectra, published optical spectra and multifrequency observations, and photoionization models. For each Seyfert galaxy, the emission-line fluxes were dereddened using the He II lambda 1640/lambda 4686 ratio. Photoionization models were calculated using a power-law index determined from the He II lambda 4686/H beta ratio; the index is very similar to that obtained from a fit to the observed multifrequency continuum from the infrared to the X-rays. The models were calculated in a way that minimized the number of assumptions, and given the uncertainties in the reddening corrections, the calculated ratios match nearly all of the dereddened ratios successfully. A multicomponent model (three components with different densities and ionization parameters) was required to fit the spectrum of I Zw 92, whereas a single component was sufficient for NGC 7674. The CNO abundances are close to solar, although a reduced abundance of up to one-third solar for one or more of the heavy elements is possible. In contrast to a previous study of Mrk 3, dust inside the NLR clouds was not required to fit the spectra of these two Seyfert galaxies, although the emission lines experience considerable reddening from external dust. Higher signal-to-noise spectra in the UV are essential for placing further restrictions on the reddening and physical conditions in the narrow-line regions of Seyfert galaxies.