A stabilized UAV recovery system is disclosed. In the illustrative embodiment for UAV recovery over water, the system includes ship-based elements and UAV-based elements. The ship-based elements include a robot arm that holds a capture mechanism over the side of the ship while compensating for wave-induced ship motion. The UAV-based elements include a hook mounted to the top of the UAV fuselage. With the capture mechanism held stable from the perspective of a UAV approaching from behind or in front of the mechanism, the UAV is flown under it, snagging an arresting line with the hook. With continued forward motion of the UAV, the arresting line pulls out of a winch drum that is coupled to a brake, bringing the UAV to rest.