This paper describes the use of magnetic levitation (MagLev) to measure the association of proteins and ligands. The method starts with diamagnetic gel beads that are functionalized covalently with small molecules (putative ligands). Binding of protein to the ligands within the bead causes a change in the density of the bead. When these beads are suspended in a paramagnetic aqueous buffer and placed between the poles of two NbFeB magnets with like poles facing, the changes in the density of the bead on binding of protein result in changes in the levitation height of the bead that can be used to quantify the amount of protein bound. This paper uses a reaction-diffusion model to examine the physical principles that determine the values of rate and equilibrium constants measured by this system, using the well-defined model system of carbonic anhydrase and aryl sulfonamides. By tuning the experimental protocol, the method is capable of quantifying either the concentration of protein in a solution, or the binding affinities of a protein to several resin-bound small molecules simultaneously. Since this method requires no electricity and only a single piece of inexpensive equipment, it may find use in situations where portability and low cost are important, such as in bioanalysis in resource-limited settings, point-of-care diagnosis, veterinary medicine, and plant pathology. It still has several practical disadvantages. Most notably, the method requires relatively long assay times and cannot be applied to large proteins (>70 kDa), including antibodies. The design and synthesis of beads with improved characteristics (e.g., larger pore size) has the potential to resolve these problems.