We here report on the modeling and characterization of adaptive microlenses. We first address device simulation with the theoretical treatment of its characterization. A follow-up paper addresses the experimental results of the focal length measurements using a simple Z-scan method. In addition, the sources of error and ways to overcome them are discussed. Previously, an adjustable electro-optic microlens with concentric electrodes was presented. The electrostatic potential was found by numerically solving Laplace's equation where the surface charge method was incorporated. The refractive index distribution within the lens aperture and the effective light path modulation was found by integration over the entire substrate thickness. We have used finite element analysis to characterize the electrostatic field distribution within the lens aperture. Unlike the previous theoretical treatment, we implement the beam propagation method to calculate the total phase delay. This will allow for accurately modeling the phase based on the optical field profile, medium inhomogeneties, and scattering and depolarization effects. Furthermore, we represent the theoretical basis for characterizing such types of lenses, and microlenses in general. In this method, we implement Fresnel diffraction and a simple Z-scan method. This technique allows for finding the lens focal length, and its sign, and study aberration effects as well.