Motion-damping systems and methods that include motion-damping systems are disclosed herein. The motion-damping systems are configured to damp relative motion between a base structure and an attached component that define a gap therebetween. The systems include an at least substantially rigid tubular structure that defines an internal volume and extends within the gap. The systems also include a magnetic assembly and a magnetically active body. One of the magnetic assembly and the magnetically active body is located within the tubular structure and the other of the magnetic assembly and the magnetically active body is operatively attached to a selected one of the base structure and the attached component. The magnetic assembly is in magnetic communication with the magnetically active body such that a magnetic interaction therebetween resists motion of the attached component relative to the base structure. The methods include dissipating energy with the motion-damping system.