The 4H-pyran-4-one (4PN) molecule serves as a model for investigating structural changes following pi* <- n electronic excitation. We have recorded the cavity ringdown (CRD) absorption spectrum of 4PN vapor at room temperature, over the wavelength region from 350 to 370 nm. This spectral region includes the T-1 (n,pi*) <- S-0 band system as well as the low-energy portion of the S-1 (n,pi*) <- S-0 system. Aided by predictions from ab initio (equation-of-motion excitation energies with dynamical correlation incorporated at the level of coupled cluster singles doubles, EOM-EE-CCSD) and density functional theory (time-dependent density functional theory with PBE0 functional, TDPBE0) calculations, we have made vibronic assignments for about 30 features in the CRD spectrum, mostly T-1 (n,pi*) <- S-0 transitions. We have used these results to correct certain vibronic assignments appearing in the previous literature for both T-1 (n,pi*) <- S-0 and S-1 (n,pi*) <- S-0 band systems. We conclude that the lowest-energy carbonyl wagging fundamentals (v(27), in-plane and v(17), out-of-plane) undergo significant frequency drops (28 and 50%, respectively) upon T-1 (n,pi*) <- S-0 excitation and similar drops (29 and 39%, respectively) for S-1 (n,pi*) <- S-0 excitation. We find that vibrational modes involving the conjugated ring atoms undergo relatively small frequency changes upon pi* <- n excitation, for both T-1 and S-1 states. We have used the present spectroscopic results and vibronic assignments to test the accuracy of computed excited-state frequencies for 4PN. This benchmarking process shows that the economical time-dependent density functional theory method is impressively accurate for certain (but not all) vibrational modes. The highly correlated EOM-EE-CCSD ab initio method is capable of making accurate frequency predictions, but the results, unexpectedly, depend sensitively on basis set family. This anomaly is traceable to a computed conical intersection between the T-1 (n,pi*) and T-2 (pi,pi*) surfaces near the T-1 (n,pi*) potential minimum. Relatively small errors in the location of the conical intersection lead to enhanced mixing of the two electronic states and incorrect T-1 (n,pi*) vibrational frequencies when certain triple-zeta quality basis sets are used.