We study the excited states of two iridium(III) complexes with potential applications in organic light-emitting diodes: fac-tris(2-phenylpyridyl)iridium(III) [Ir(ppy)3] and fac-tris(1-methyl-5-phenyl-3-n-propyl-[1,2,4]triazolyl)iridium(III) [Ir(ptz)3]. Herein we report calculations of the excited states of these complexes from time-dependent density functional theory (TDDFT) with the zeroth-order regular approximation (ZORA). We show that results from the one-component formulation of ZORA, with spin–orbit coupling included perturbatively, accurately reproduce both the results of the two-component calculations and previously published experimental absorption spectra of the complexes. We are able to trace the effects of both scalar relativistic correction and spin–orbit coupling on the low-energy excitations and radiative lifetimes of these complexes. In particular, we show that there is an indirect relativistic stabilisation of the metal-to-ligand charge transfer (MLCT) states. This is important because it means that indirect relativistic effects increase the degree to which SOC can hybridise singlet and triplet states and hence plays an important role in determining the optical properties of these complexes. We find that these two compounds are remarkably similar in these respects, despite Ir(ppy)3 and Ir(ptz)3 emitting green and blue light respectively. However, we predict that these two complexes will show marked differences in their magnetic circular dichroism (MCD) spectra.