The need to limit the population of artificial debris in near-Earth space motivates the development of efficient deorbiting propulsion systems. Electrodynamic tethers offer a valid and attractive alternative to conventional chemical thrusters because they impose a penalty in terms of deorbiting time rather than additional launch mass. A low-cost demonstration mission is designed, where a reduced-scale deorbiting system will be carried, deployed, and controlled by a microsatellite. Numerical simulations show that the proposed configuration of the electrodynamic system allows, even in absence of active tether current control, to maintain a stable tether attitude motion. This is obtained through a careful combination of bare and insulated tether segments. When active current control is applied, the tether libration angles are bounded to within 10 deg. The closed-loop control laws make use of the in-plane and out-of-plane libration angles and rates, which are estimated through a newly developed extended Kalman filter. The estimator's measurements are provided by two three-axis magnetometers mounted on the spacecraft structure and at the lower tether endpoint, respectively. It is shown that this microsystem is able to deorbit a low-Earth-orbit carrier spacecraft in about two months, demonstrating salient features of tether technologies and associated electrodynamic effects.