In this paper, we consider the use of dimensional analysis for modeling electromagnetic levitation and braking problems, which are described by the Lorentz force law. Based on Maxwell's equations, to illustrate the underlying field problem, we formulate a complete mathematical model of a simple academic example, where a permanent magnet is moving over an infinite plate at constant velocity. The step-by-step procedure employed for dimensional analysis is described in detail for the given problem. A dimensionless model with a reduced number of parameters is obtained, which highlights the dominant dependences, and it is invariant to the dimensional system employed. Using the dimensionless model, a concise parametric study is conducted to illustrate the advantages of the dimensionless representation for displaying complex data in an efficient manner. We provide an exhaustive study of the dependences of the Lorentz force on the dimensionless parameters to complete the analysis, and we give results for a generalized representation of the problem. Finally, scaling laws are derived and illustrated based on practical examples.