Time-resolved ZEKE (zero electron kinetic energy) spectroscopy has enabled measurements of the rates of decay of molecular Rydberg states close to (within a few cm-1 of) the ionization threshold. The ion yield as a function of photon energy in this region cannot be understood without knowing both the ionization potential and the principal quantum numbers, n, of the states involved. Unfortunately, these two unknowns are linked by the equation hnu = IP - R/(n - delta)2; an independent method must be used to measure the ionization potential, IP. We have found two molecules appropriate for these measurements, bis(benzene)chromium (BBC) and diazacyclooctane (DABCO), both of which have very long Rydberg series with resolved transitions up to n = 35 (BBC) and n = 70 (DABCO). Highly accurate values of the ionization potential (+/- 0.5 cm-1) were obtained by extrapolating these series. The line widths are shown to decrease with increasing n with a power of n of 2.5 +/- 0.3. These are the first measurements of the n dependence of the nonradiative rates over a large range of n for polyatomic molecules in Rydberg states. However, one cannot simply extrapolate the lifetimes (as determined from the widths) to the region near the ionization threshold where the n = 100-200 states are being excited. There the lifetimes as determined directly by ZEKE spectroscopy are longer by several orders of magnitude than the values obtained by extrapolation.