The ISO coronal line spectrum of a sample of the brightest known Seyfert galaxies is presented and modeled. ISO observations of [O IV] 25.9 μ, [Ne V] 14.3 μ, [Mg VIII] 3.02 μ and [Si IX] 2.58 μ lines are presented; their relationship with 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 as the intrinsic shape of the UV ionizing spectrum. However, for the brightest Seyferts analyzed, NGC 1068, Circinus and NGC 4151, a blackbody UV continuum is favored.