We apply a wide range of correlated electronic structure approaches to the excited states of Ni(CO)4 and Ni(CO) as model complexes of saturated and unsaturated transition metal carbonyls respectively to understand the performance of each method, in addition to setting benchmark data for these metal carbonyls. In particular, we apply the coupled-cluster linear response hierarchy, complete-active-space self-consistent field theory, N-electron valence state multireference perturbation theory, Monte Carlo configuration interaction, and time-dependent density functional theory with a range of functionals and basis sets. We find that although the systems can qualitatively be described by a single configuration, electron correlation effects are sufficiently strong to give large single amplitudes in cluster expansions, which cause spurious solutions to the response equations for the intermediate CCn methods. DFT also performs well if care is taken to choose an appropriate functional, although for Ni(CO) several popular functionals give the incorrect ground spin-state, depending on the amount of Hartree-Fock exchange.