ABSTRACT Upcoming observations will probe the first billion years of our Universe in unprecedented detail. Foremost among these are 21-cm interferometry with the Hydrogen Epoch of Reionization Arrays (HERA) and the Square Kilometre Array (SKA), and high-z galaxy observations with the James Webb Space Telescope (JWST). Here, we quantify how observations from these instruments can be used to constrain the astrophysics of high-z galaxies. We generate several mock JWST luminosity functions (LFs) and SKA1 21-cm power spectra, which are consistent with current observations, but assume different properties for the unseen, ultrafaint galaxies driving the epoch of reionization (EoR). Using only JWST data, we predict up to a factor of 2–3 improvement (compared with Hubble Space Telescope, HST) in the fractional uncertainty of the star formation rate to halo mass relation and the turnover magnitude. Most parameters regulating the ultraviolet (UV) galaxy properties can be constrained at the level of ∼10 per cent or better, if either (i) we are able to better characterize systematic lensing uncertainties than currently possible; or (ii) the intrinsic LFs peak at magnitudes brighter than MUV ≲ −13. Otherwise, improvement over HST-based inference is modest. When combining with upcoming 21-cm observations, we are able to significantly mitigate degeneracies, and constrain all of our astrophysical parameters, even for our most pessimistic assumptions about upcoming JWST LFs. The 21-cm observations also result in an order of magnitude improvement in constraints on the EoR history.