The present study of the ordering of apolar molecules dissolved in uniaxial mesophases has been carried out by a model where the interactions between the solute and the local medium are described on a molecular scale. On the contrary, the mutual interactions between the solvent molecules are not explicitly taken into account, but a mean description of the macroscopic anisotropy of the bulk of the solvent is provided. This is done by defining a "virtual" mesophase director whose instantaneous orientation in the solute molecular frame is randomly given step-by-step during the numerical calculation of the solute order parameters. This model has been applied to apolar molecules biphenylene, 1,4-dicyanobenzene, 1,4-dinitrobenzene, and p-benzoquinone. The predicted order parameters have been compared with the H-1 NMR experimental data obtained for the same compounds dissolved in nematic solvents EBBA and ZLI1132 and in the 55 wt % ZLI1132 + EBBA magic mixture, where long-range effects are believed to be very small. A nearly perfect matching of the simulated solute-ordering matrices with the data in the magic mixture has been found, thus strengthening the common assumption that long-range effects can be neglected in that mixture. The model has also been tested on so-called magic solutes cyclohexane, 1,4-trans-dimethylcyclocyclohexane, and trans-decalin (whose electronic structure should preclude significant anisotropic long-range interactions) dissolved in ZLI2452. Once more, we obtained excellent results in reproducing the experimental order parameters (Terzis, A. F.; Poon, C.-D.; Samulski, E. T.; Luz, Z.; Poupko, R.; Zimmermann, H.; Muller, K.; Toriumi, H.; Photinos, D. J. J. Am. Chem. Soc. 1996, 118, 2226) over a very large range of temperatures, and this is a further evidence of the validity of the approach.