Motivated by the discrepancies in recent experimental and theoretical studies of photodetachment from isolated model chromophores of the green fluorescent protein (GFP), this study reports calculations of the electron detachment energies and photoelectron spectra of the phenolate and deprotonated p-hydroxybenzylidene-2,3-dimethylimidazolinone (HBDI) anions. The spectra were computed using double-harmonic parallel normal mode approximation. High-level coupled-cluster methods as well as density functional theory were used to compute vertical and adiabatic detachment energies of the phenolate anion serving as a model system representing anionic GFP-like chromophores (HBDI). The benchmark calculations reveal that the basis set has significant effect on the computed detachment energies, whereas the results are less sensitive to the level of electron correlation treatment. At least aug-cc-pVTZ basis set is required. The best omega B97X-D and CCSD(T) estimates of phenolate's adiabatic detachment energy are 2.12 and 2.19 eV; these values are very close to the experimental value, 2.253 eV [Gunion et al. Int. J. Mass Spectrom. Ion Proc. 1992, 117, 601]. The best estimate of the vertical detachment energy of deprotonated HBDI is 2.76 eV, which supports bound character of the bright excited state in the Franck-Condon region. The most intense transition in the computed photoelectron spectra of both phenolate and deprotonated HBDI is the 0-0 S-0-D-0 transition, which is 0.11 eV below vertical detachment energy. Therefore, the position of the maximum of the photoelectron spectrum does not represent vertical detachment energy, and the direct comparison between theory and experiment must involve spectrum modeling.