Abstract: The possibility of a contactless capture of the conductive space-debris objects (SDOs) using electromagnetic induction based on Faraday’s law of induction and Lenz’s law is analyzed. It is assumed that the spacecraft (SC) for capturing SDOs is equipped with a toroidal coil, which generates a sufficiently strong magnetic field and induces it on the SDO approaching the SC. The dynamics of the orbital motion of the SDO relative to the SC is modeled using the Clohessy–Wiltshire equations and studied numerically. The proposed method for the contactless electromagnetic capture of the conductive SDO can be used to move the SDO to a target orbit—in particular, to a graveyard orbit. The feasibility of the method is discussed based on modeling results. Directions for improvement and development of the method are identified.