We present a new multiwavelength study of supernova remnant (SNR) B0513-692 in the Large Magellanic Cloud (LMC). The remnant also has a strong, superposed, essentially unresolved, but unrelated radio source at its north-western edge, J051324-691049. This is identified as a likely compact H ii region based on related optical imaging and spectroscopy. We use the Australia Telescope Compact Array (ATCA) at 4790 and 8640 MHz (λ ≃ 6 cm and λ ≃ 3.5 cm) to determine the large-scale morphology, spectral index and polarization characteristics of B0513-692 for the first time. We detect a strongly polarized region (49 per cent) in the remnant's southern edge (λ ≃ 6 cm). Interestingly, we also detect a small (∼40 arcsec) moderately bright, but distinct optical, circular shell in our Hα imagery which is adjacent to the compact H ii region and just within the borders of the north-eastern edge of B0513-692. We suggest that this is a separate new SNR candidate based on its apparently distinct character in terms of optical morphology in three imaged emission lines and indicative SNR optical spectroscopy (including enhanced optical [S ii] emission relative to Hα).