AbstractAs the remnant of Supernova (SN) 1987A has been getting brighter over time, new observations at high frequencies have allowed imaging of the radio emission at unprecedented detail. We present a new radio image at 44 GHz of the supernova remnant (SNR), derived from observations performed with the Australia Telescope Compact Array (ATCA) in 2011. The diffraction-limited image has a resolution of 349×225 mas, which is the highest achieved to date in high-dynamic range images of the SNR. We also present a new image at 18 GHz, also derived from ATCA observations performed in 2011, which is super-resolved to 0″.25. The new 44 and 18 GHz images yield the first high-resolution spectral index map of the remnant. The comparison of the 44 GHz image with contemporaneous X-ray and Hα observations allows further investigations of the nature of the remnant asymmetry and sheds more light into the progenitor hypotheses and SN explosion. In light of simple free-free absorption models, we discuss the likelihood of detecting at 44 GHz the possible emission originating from a pulsar wind nebula (PWN) or a compact source in the centre of the remnant.