The Infrared Space Observatory (ISO) coronal line spectrum of the brightest Seyfert galaxies from the CfA sample is presented and modeled. ISO observations of [O IV] 25.9 μm, [Ne V] 14.3 μm, [Mg VIII] 3.02 μm, and [Si IX] 2.58 μm lines are presented; their relationship with the soft part of the ionizing spectrum from 50 to 300 eV is investigated. Pure photoionization models reproduce the line ratios, setting ranges for the ionization parameter and the optical depth of the emitting clouds. On the basis of the available data alone it is not possible to distinguish between a power-law or a blackbody distribution as the intrinsic shape of the UV-ionizing spectrum. However, for the brightest Seyfert galaxies analyzed, namely, NGC 1068, Circinus, and NGC 4151, a blackbody UV continuum is favored.