This thesis examines the dynamics of the formation of tethers, which are tubes of lipids 20 - 200 nm in diameter. In particular, this work investigates how the loading rate affects the observed threshold force at which a tether forms from a vesicle membrane. Tether dynamics are important to a myriad of biological processes such as signaling when white blood cells adhere to the walls of healthy and diseased blood vessels, or in the transport of intracellular material between neighboring cells. To understand the dynamics of tether formation in such systems more fully, the studies presented in this thesis focus on the dependence of the force needed to create a tether on the rate of force change. To conduct these experiments, I combined, for the first time, a microfabricated magnetic force transducer, or a microscale device that generates well-controlled and localized magnetic fields, and microaspiration, a technique to apply known tension to a lipid membrane. Using the combined global and local mechanical control of the joint system, I discovered a strong correlation between the threshold force of tether formation and the applied force ramp. An energy model, based upon that used to describe membrane rupture, characterized the observed dependencies and provided a mechanism to examine physically relevant quantities within the system. The usefulness of this combined approach was further substantiated by determining the influence of membrane modulators, including cholesterol, tension, adhesion site concentration, and phosphatidylserine, on the dependence seen between force threshold and force rates. Additionally, application of the experimental technique developed in this thesis led to the calculation of the inter-layer drag coefficient between membrane leaflets and to the first measurements of the thermal expansivity in aspirated 1-stearoy1-2-oleoyl- sn -glycero-3-phosphatidylcholine vesicles. This new tool for dynamic studies of membrane mechanics may further be extended to study how tethers form off of flowing cells or how phase regimes, induced by the presence of cholesterol, influence membrane dynamics.