Accurate predictions of photoexcitation properties are a major challenge for modern methods of theoretical chemistry. We show here how approximate coupled-cluster singles and doubles (CC2) calculations in combination with the reduced virtual space (RVS) approach can be employed in studies of excited states of large biomolecular systems. The RVS-CC2 approach is used for accurately predicting optical properties of the p-hydroxybenzylidene-dihydroimidazolinone (p-HBDI) chromophore embedded in green fluorescent protein (GFP) models using quantum mechanical calculations in combination with large basis sets. We study the lowest excited states for the isolated and protein-embedded chromophore in two different protonation states, and show how omitting high-lying virtual orbitals in the RVS calculation of excitation energies renders large-scale CC2 studies computationally feasible. We also discuss how the error introduced by the RVS approach can be systematically estimated and controlled. The obtained CC2 excitation energies of 3.13-3.27 and 2.69-2.77 eV for the two protonation states of different protein models are in excellent agreement with the maxima of the experimental absorption spectra of 3.12-3.14 and 2.61-2.64 eV, respectively. Thus, the calculated energy splitting between the excited states of the two protonation states is 0.44-0.52 eV, which agrees very well with the experimental value of 0.48-0.51 eV. The calculations at the RVS-CC2 level on the protein models show the importance of using large QM regions in studies of biochromophores embedded in proteins.