Snow density data are important for a variety of applications, yet, to our knowledge, there are no robust methods for estimating spatiotemporal varying snow density in the Arctic environment. The current understanding of snow density variability is largely limited to manual <em>in situ</em> sampling, which is not feasible across large domains like the Canadian Arctic. This research proposes a passive microwave retrieval algorithm for tundra snow density. A two-layer electromagnetic snowpack model, representing depth hoar underlaying a wind slab layer, was used to estimate microwave emissions for use in an inverse model to estimate snow density. The proposed algorithm is predicated on solving the inverse model at boundary conditions for the snowpack layer densities to estimate snow density within a plausible range. An experiment was conducted to assess the algorithm’s ability to reproduce snow density estimates from snow courses at four high arctic sites in the Canadian tundra. The electromagnetic snowpack model was calibrated at one site and then evaluated at the three other sites. Results from the calibration and evaluation sites were similar and the algorithm replicated the density estimates from snow courses well with absolute error values approaching the uncertainty of the reference data (±10 %). The algorithm configuration appears best suited for estimating snow density conditions towards the end of the winter season. With more extensive forcing data (e.g. from global climate models) this algorithm could be applied across the tundra to provide information on snow density at scales that are not currently available.