This thesis is based on multi-wavelength observations of supernova remnants in the nearby Sculptor Group galaxy NGC 300. A survey of the literature provides a set of observations of supernova remnants and candidate supernova remnants within NGC300 in the x-ray, optical and radio spectral regions. A radio survey published by Payne et al. (2004) presents a number of new candidate supernova remnants. Blair & Long (1997) published an optical survey of supernova remnant candidates that have not been re-observed before this thesis and some of which had never had optical spectra taken. These two candidate sets were used to create a set of objects which were observed with the Advanced Technology Telescope at Siding Spring Observatory, using its moderate-resolution (< 5 angstroms) dual-beam spectrometer (Millar et al., 2011). Most of the radio sources of Payne et al. (2004) did not meet the accepted optical requirement of [SII]:H-alpha > 0.4 while most of the optical sources from Blair & Long (1997) did meet this requirement. With multiple sources of observations of the optical supernova remnant candidates (Blair & Long, 1997) a problem appears. Comparing observations of the supernova remnant candidate labelled N300-S16 made by Blair & Long (1997) with those published in Millar et al. (2011) and also compared with an archival observation from the Hubble Space Telescope provides conflicting evidence as to the true nature of this particular object. Although there are known problems with the [SII]:H-alpha > 0.4 criterion for identifying supernova remnants and there are reported resolutions to these problems, there appear to be more problems that may as yet be unrecognised. The spectral line flux levels from N300-S16 are low and this may cause a large error in spectral line flux measurement. This error source was investigated in Millar et al. (2011). The sulphur/oxygen gradient of NGC 300 has been studied (Christensen et al., 1997) and NGC 300 has a high level of diffuse ionised gas (Hoopes et al., 1996). There are no studies into how these factors may affect the [SII]:H-alpha measurements for object identification. Telescope pointing errors, astrometry errors and seeing conditions all act adversely to the correct measurement of flux density from extragalactic candidate supernova remnants. The effects of these errors were investigated in particular for the N300-S16 object. I find that other observation techniques may be needed along with optical spectra -- preferably very high-resolution optical imaging with space-based or ground-based adaptive optics capable telescopes -- to confirm the true identity or even to validate the existence of some extragalactic supernova remnants. In the process of comparing Hubble Space Telescope images of NGC 300 with radio emission sources consistent with supernova remnants, I have found four locations where the Hubble Space Telescope's images support the radio sources as being supernova remnants.