A general model for the Wilhelmy (fiber) surface tension measurement method for uniaxial nematic liquid crystals has been derived using fundamental principles and classical liquid-crystal physics. A rigorous formulation of the contributions of surface and bulk nematic elasticity was implemented for the Wilhelmy method. The surface contribution is a function of the surface anchoring strength of the liquid-crystal free surface and the director surface orientation at the solid-nematic-vapor common line. The exact bulk elasticity contribution is a function of the director field in the meniscus, which is a function of the nematic-fiber interactions, the size of the fiber, and the temperature, among other things. The specific form of the Wihelmy model equation for four typical nematic textures was developed and analyzed. It is found that the effect may depend on the size of the fiber, the presence of disclinations, and the representative Frank elastic constants. The expression representing the actual measurement or apparent surface tension was derived and used to identify the exact nature of the nematic contributions for typical nematic textures. Identification of material systems, experimental conditions, and geometric factors that enhance the impact of nematic ordering on the Wilhelmy surface tension measurements was given. A qualitative comparison of the model prediction with experimental data highlights the utility of the derived equations.