Millimetre and submillimetre photometry of four galaxies with bright compact infrared nuclei is presented. The two galaxies with starburst nuclei have 60 micron-1 mm spectra well fitted by isothermal emission from cool (~35 K) dust grains with a v^2^ emissivity dependence and no evidence of emission from a much colder dust component. Non-thermal nuclear emission and free-free emission arising from the nuclear H II regions become significant at wavelengths longer than 1 mm, where they can make a measurable contribution to the flux. The Seyfert galaxy Mrk 231 shows clear excess emission beyond 1 mm above the dust continuum fitted to the far-infrared and submillimetre photometry. This component has a flux level that is consistent with an extrapolation of the radio spectrum attributed to synchrotron emission. The data on the heavily obscured nucleus of NGC 4418 are more ambiguous. Adequate representations of the far-infrared to millimetre dust emission can be obtained with a dust emissivity dependence of between v and v^2^, depending upon the dust opacity adopted at far-infrared wavelengths. The photometry shows a weak excess above the dust continuum at wavelengths beyond 1300 microns, which can partially be accounted for by an extrapolation of the radio spectrum; the residual excess may be due to free-free emission. By equating the sizes of the dust emission regions to those of the compact radio cores in these galaxies, fits to the dust emission spectra are obtained that are optically thick at mid- and far-infrared wavelengths in Mrk 231 and NGC 4418, but which are in approximate agreement with the extinction estimated from the 9.7-micron silicate absorption features. While there is no evidence of emission from a cold (<20 K) dust component in any of these galaxies, the uncertainties in the source size and the dust opacity law at long wavelengths limit the accuracy with which the dominant cool dust components can be described.