We calculate the lowest ionisation and excitation energies in a variety of biologically important molecules, i.e. π-conjugated systems like DNA and RNA bases and isomers plus related heterocyclic molecules. For approximately half of these molecules, there are no experimental and theoretical/numerical data in the literature, as far as we know. These electronic transitions are mainly but not exclusively of π and π–π* character, respectively. We perform symmetry-constrained density functional theory (DFT) geometry optimisation at the B3LYP/6-311++G** level of theory. At the DFT-obtained ground-state geometries, we calculate vertical ionisation energies with ionisation potential coupled cluster with singles and doubles (IP-EOMCCSD) and vertical excitation energies with the completely renormalised equation of motion coupled cluster with singles, doubles, and non-iterative triples (CR-EOMCCSD(T)) method. We also investigate whether a simple semi-empirical Hückel-type model approach with novel parametrisation could provide reasonable estimates of the lowest π ionisation and π–π* excitation energies. Our coupled cluster (CC) results are in very good agreement with experimental data, while the Hückel-type model predictions generally follow the trends with some deviation. Finally, we investigate the effect of basis set in IP-EOMCCSD energies and we compare our CR-EOMCCSD(T) results with time-dependent DFT (TDDFT) ones.