The 4H-pyran-4-one (4PN) molecule serves as a model for investigating structural changes following π* ← 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 T1(n,π*) ← S0 band system as well as the low-energy portion of the S1(n,π*) ← S0 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 T1(n,π*) ← S0 transitions. We have used these results to correct certain vibronic assignments appearing in the previous literature for both T1(n,π*) ← S0 and S1(n,π*) ← S0 band systems. We conclude that the lowest-energy carbonyl wagging fundamentals (ν27, in-plane and ν17, out-of-plane) undergo significant frequency drops (28 and 50%, respectively) upon T1(n,π*) ← S0 excitation and similar drops (29 and 39%, respectively) for S1(n,π*) ← S0 excitation. We find that vibrational modes involving the conjugated ring atoms undergo relatively small frequency changes upon π* ← n excitation, for both T1 and S1 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 T1(n,π*) and T2(π,π*) surfaces near the T1(n,π*) potential minimum. Relatively small errors in the location of the conical intersection lead to enhanced mixing of the two electronic states and incorrect T1(n,π*) vibrational frequencies when certain triple-ζ quality basis sets are used.