Electronic absorption and emission spectra of [M25(MPA)18]- (M = Au, Ag; MPA = SCH2CH2COOH) clusters have been recorded for energies below 5 eV at the time-dependent density functional theory (TDDFT) level using B3LYP and TPSSh functionals and compared to the calculated ones using the computationally inexpensive simplified TDDFT (sTDDFT) approach. The results show a qualitative agreement between the TDDFT and sTDDFT approaches used here, which were also in line with the experimental and theoretical spectra previously reported. However, the sTDDFT calculations were several orders of magnitude faster than those obtained by TDDFT. Our results support that sTDDFT provides an excellent balance between accuracy and low computational cost, becoming a suitable approach for studying the absorption and emission spectra of noble-metal clusters of sizes that would be unaffordable by the traditional TDDFT methods. The main peaks of the experimental absorption spectrum of [Au25(MPA)18]- have been previously assigned, whereas [Ag25(MPA)18]- has not been synthesised. However, its absorption spectrum resulted in having similar features to the experimental spectrum of [Ag25(GSH)18]- (GSH = glutathione), used to validate our results. The emission spectra, which to date have not been reported either from experimental or theoretical means, were simulated by using the molecular structure of the first excited triplet state (T1). The emission spectra were obtained by comparing them to those of [M25(GSH)18]- since no experimental luminescence spectra have been reported for [M25(MPA)18]-. The calculations suggest that [Ag25(SR)18]- (SR = thiolate) clusters have a weak luminescence band in the NIR region. Finally, solvent shifts were found to be minor, whereas the absorption bands seem to be significantly redshifted in solid-state materials.