Practical applications of guest-host liquid crystal systems are critically dependent on the alignment of the guest species within the liquid crystal host. UV/Vis absorption spectroscopy shows that the 1,5-dihydroxy-2,6-bis-(4-propylphenyl)-9,10-anthraquinone dye aligns within the E7 nematic host, giving an experimental dichroic ratio of 9.40 and dye order parameter of 0.74. This alignment was modelled by using a combination of density functional theory (DFT) and molecular dynamics (MD) computational approaches that do not require the input of experimental data. Time-dependent DFT calculations show that the electronic transition dipole moment is highly aligned with the long molecular axis of the dye. Fully atomistic MD simulations show that the long axis of the dye is less highly aligned within the E7 host, indicating that this contribution limits the overall dye alignment and, thereby, the potential practical applications of this particular system. Importantly, this study demonstrates an experimental and combined DFT and MD computational approach that may be applied generally to guest-host systems, providing a potential route to their rational design. Model guest: A guest anthraquinone dye that aligns within a nematic liquid crystal host is modelled by a combined computational approach. DFT calculations give the alignment of the transition dipole moment within the dye, and fully atomistic MD simulations model the alignment of the dye within the host.