The material properties of biomembranes can be measured by forming a tether, a thin bilayer tube that extends from the membrane surface. The force required to maintain a tether at a given length depends upon both membrane properties as well as the mechanical, chemical and electrical environment. To characterize membrane material properties and responses, the influences of electromechanical energy, interfacial phenomena, and thermally-driven entropic tensions are considered in separate, thermodynamic models of tether formation. To determine how electric fields influence tether behavior, the energetic contributions arising from Maxwell stresses as well as from flexoelectric and piezoelectric coupling are included in an analysis of tether formation from an aspirated vesicle. For typical membrane elctromechanical coefficients, flexoelectric coupling alters the force required to form a tether of a given length, while piezoelectric coupling and Maxwell forces do not greatly change the force vs. tether length behavior. Given recent experiments demonstrate tethers formed from cellular membranes are sensitive to the transmembrane potential, an analysis is developed to characterize the electromechanical properties of unaspirated cellular membranes. Both flexoelectric and piezoelectric coupling energies as well as the voltage sensitivity of the interfacial tension and bending stiffness are included in the analysis. For typical membrane charge densities, small changes in tether force are calculated for the contributions of the interfacial phenomena. Inclusion of the electromechanical coupling energies leads to experimentally observable changes in tether force. These analyses are applied to determine the mechanism by which the motor protein prestin confers electromotility to the outer hair cell (OHC) of the mammalian cochlea. For the values of electromechanical coupling coefficients obtained from OHC deformation models, the tether force increases with depolarization for flexoelectric coupling and decreases for piezoelectric coupling. Since cellular membranes are typically under small entropically-driven tensions, the influence of thermally driven surface undulations on tether conformation is considered. By fitting the model to experimental tether data, the tension of a vesicle can be determined. The analyses developed in this thesis provide novel methods to determine many otherwise difficult to characterize membrane material properties and, thus, help to deepen understanding of the behavior of cellular membranes.