Human perception of material colors depends heavily on the nature of the light sources that are used for illumination. One and the same object can cause highly different color impressions when lit by a vapor lamp or by daylight, respectively. On the basis of state-of-the-art colorimetric methods, we present a modern approach for the calculation of color-rendering indices (CRI), which were defined by the International Commission on Illumination (CIE) to characterize color reproduction properties of illuminants. We update the standard CIE method in three main points: first, we use the CIELAB color space; second, we apply a linearized Bradford transformation for chromatic adaptation; and finally, we evaluate color differences using the CIEDE2000 total color difference formula. Moreover, within a real-world scene, light incident on a measurement surface is composed of a direct and an indirect part. Neumann and Schanda [Proc. CGIV'06 Conf., Leeds, UK, pp. 283-286 (2006)] have shown for the cube model that diffuse interreflections can influence the CRI of a light source. We analyze how color-rendering indices vary in a real-world scene with mixed direct and indirect illumination and recommend the usage of a spectral rendering engine instead of an RGB-based renderer for reasons of accuracy of CRI calculations.