Complex behaviors are mediated by neural computations occurring throughout the brain. In recent years, tremendous progress has been made in developing technologies that can record neural activity at cellular resolution at multiple spatial and temporal scales. However, these technologies are primarily designed for studying the mammalian brain during head fixation - wherein the behavior of the animal is highly constrained. Miniaturized devices for studying neural activity in freely behaving animals are largely confined to recording from small brain regions owing to performance limitations. We present a cranial exoskeleton that assists mice in maneuvering neural recording headstages that are orders of magnitude larger and heavier than the mice, while they navigate physical behavioral environments. Force sensors embedded within the headstage are used to detect the mouse's milli-Newton scale cranial forces which then control the x, y, and yaw motion of the exoskeleton via an admittance controller. We discovered optimal controller tuning parameters that enable mice to locomote at physiologically realistic velocities and accelerations while maintaining natural walking gait. Mice maneuvering headstages weighing up to 1.5 kg can make turns, navigate 2D arenas, and perform a navigational decision-making task with the same performance as when freely behaving. We designed an imaging headstage and an electrophysiology headstage for the cranial exoskeleton to record brain-wide neural activity in mice navigating 2D arenas. The imaging headstage enabled recordings of Ca2+ activity of 1000s of neurons distributed across the dorsal cortex. The electrophysiology headstage supported independent control of up to 4 silicon probes, enabling simultaneous recordings from 100s of neurons across multiple brain regions and multiple days. Cranial exoskeletons provide flexible platforms for largescale neural recording during the exploration of physical spaces, a critical new paradigm for unraveling the brain-wide neural mechanisms that control complex behavior.