The stringent stability requirements imposed by advanced, high-resolution payloads have produced an increased interest in the development of better-performing micro-vibration isolators. Several devices aimed at mitigating micro-vibrations have been studied and implemented, but their application is still far from being ideal due to the several drawbacks that they present, such as limited low-frequency attenuation for passive systems or high power consumption and reliability issues for active systems. This research focuses on the modelling and testing of Electromagnetic Shunt Dampers (EMSD) characterised by the use of negative impedance converter circuits. An electromagnetic damper is a self-excited device that exploits the interaction between a moving magnetic field and a conductive material to provide a reaction force to the applied motion. An EMSD presents several advantages, but the high ratio of system mass over damping force produced has limited its application in space missions. The use of a negative resistance can considerably lower this ratio since it produces an overall reduction of the circuit resistance that results in an increase of the induced current in the closed circuit and thus the damping performance. In this thesis, the development of a multiphysics, multi-parametric model of an EMSD is presented and accurately corroborated by an extensive test campaign. This damper can be classified as a semi-active damper since the negative resistance circuit does not require any control algorithm to operate. In terms of damping performance, this research demonstrates that an EMSD applied to a 1-DoF system is capable of behaving, throughout the whole temperature range of interest, like a 2nd-order mechanical filter in which the resonance peak is eliminated and the roll-off slope is -40 dB/dec. Additionally, the proposed EMSD is characterised by low required power, simplified electronics and small device mass that could allow it to be comfortably integrated on a satellite. This study presents also a possible novel 2-collinear-DoF system design with embedded EMSDs. This isolator is capable of achieving a remarkable final decay rate of -80 dB/dec while completely eliminating the two resonance peaks due to the high attenuation performance of the dampers. Moreover, other aspects of the proposed 2-collinear-DoF system are investigated in order to assess not only the damping performance but also its features at system level. This work demonstrates that the fundamental advantages of this system can make it a viable, competitive alternative to other actively controlled struts.