The ability to track handheld controllers in 3D space is critical for interaction with head-mounted displays, such as those used in virtual and augmented reality systems. Today's systems commonly rely on dedicated infrastructure to track the controller or only provide inertial-based rotational tracking, which severely limits the user experience. Optical inside-out systems offer mobility but require line-of-sight and bulky tracking rings, which limit the ubiquity of these devices. In this work, we present Aura, an inside-out electromagnetic 6-DoF tracking system for handheld controllers. The tracking system consists of three coils embedded in a head-mounted display and a set of orthogonal receiver coils embedded in a handheld controller. We propose a novel closed-form and computationally simple tracking approach to reconstruct position and orientation in real time. Our handheld controller is small enough to fit in a pocket and consumes 45 mW of power, allowing it to operate for multiple days on a typical battery. An evaluation study demonstrates that Aura achieves a median tracking error of 5.5 mm and 0.8 degrees in 3D space within arm's reach.