A 1,5-diphenylythio-substituted anthraquinone, two 1,5-diphenylamino-substituted anthraquinones, and two 2,6-diphenyl-substituted anthraquinones have been studied in the context of the dyes as guests in nematic liquid crystal hosts, using a range of experimental and computational techniques. UV-visible absorption spectroscopy showed that the dyes exhibit visible transitions at a range of wavelengths, and polarised UV-visible absorption spectroscopy of aligned samples of the dyes in the nematic host E7 yielded a range of dichroic order parameters. Redox potentials of the dyes obtained by cyclic voltammetry and spectroelectrochemistry showed significantly more variation between the oxidation potentials than the reduction potentials, and a correlation between colour and redox properties was shown. Visible electronic transitions were calculated by time dependent density functional theory, and order parameter contributions determined from angles between the calculated transition dipole moment orientations and the minimum moment of inertia axes matched the trend in experimental dichroic order parameters. Molecular dynamics simulations of the dyes in E7 showed little variation in calculated orientational order parameters of the minimum moment of inertia axes of the dyes. The trend in experimental dichroic order parameters was replicated by calculated values, determined by combining the calculated orientational order parameters with the contributions from the transition dipole moment orientations. An assessment of various molecular alignment axes of the dyes indicated that the surface tensor model provided the most aligned axes of those tested, and improved the match with experimental dichroic order parameters. Incorporating dye flexibility into the calculations resulted in a further improvement in the match with experiment. Isolated molecule simulations combined with a mean field approach enabled the calculation of order parameters at a reduced computational expense. Application of this approach to a variety of dyes from different classes demonstrated a generally good match with reported experimental alignment trends.