In this paper we consider whether an animal or an agent (a `shadower') can actively camouflage its movements whilst tracking another animal or agent (a `shadowee'). It is shown that, under certain conditions, the shadower can conceal its motion if it moves along a trajectory such that it emulates the optic flow produced by a stationary object, as viewed by the moving shadowee. Algorithms for determining trajectories which enable the shadower to camouflage its motion whilst tracking a shadowee, or whilst moving toward a stationary or moving target, are developed and tested. The proposed strategies work regardless of whether the shadower is viewed against a homogeneous or a structured background. It is of interest to investigate the relevance of active motion camouflage in contexts such as `shadowing' behaviour in hoverflies, capture of prey by predators and military manoeuvres.