We present the first detailed study of the spatially resolved dust continuum emission of simulated galaxies at 1 < z < 5. We run the radiative transfer code skirt on a sample of submillimetre-bright galaxies drawn from the Feedback In Realistic Environments (FIRE) project. These simulated galaxies reach Milky Way masses by z = 2. Our modelling provides predictions for the full rest-frame far-ultraviolet-to-far-infrared spectral energy distributions of these simulated galaxies, as well as 25-pc resolution maps of their emission across the wavelength spectrum. The derived morphologies are notably different in different wavebands, with the same galaxy often appearing clumpy and extended in the far-ultraviolet yet an ordered spiral at far-infrared wavelengths. The observed-frame 870-μm half-light radii of our FIRE-2 galaxies are ∼0.5−4kpc, consistent with existing ALMA observations of galaxies with similarly high redshifts and stellar masses. In both simulated and observed galaxies, the dust continuum emission is generally more compact than the cold gas and the dust mass, but more extended than the stellar component. The most extreme cases of compact dust emission seem to be driven by particularly compact recent star formation, which generates steep dust temperature gradients. Our results confirm that the spatial extent of the dust continuum emission is sensitive to both the dust mass and star formation rate distributions.