ABSTRACT We present a spatially resolved study of the kinematical properties of known supernova remnants (SNRs) in the nearest galaxies of the SIGNALS survey, namely NGC 6822 (one object) and M33 (163 objects), based on data obtained with the SITELLE imaging Fourier transform spectrometer at the Canada–France–Hawaii Telescope. The purpose of this paper is to provide a better scheme of identification for extragalactic SNRs and, in particular, to distinguish between H ii regions and SNRs. For that we have used diagrams which involve both the [S ii]/H$\alpha$ ratio and the velocity dispersion ($\sigma$). We also introduce a new parameter, $\xi = {[\rm S\, {\small II}] \over H\alpha } \times \sigma$, which enhances still the contrast between SNRs and the rest of the ionized gas. More than 90 per cent of the SNRs in our entire sample show an integrated [S ii]/H$\alpha$ ratio larger than the canonical value (0.4). 86 per cent of the SNRs present in our field show a significant velocity dispersion. The spectral resolution of our observations allows us to observe the complex velocity structure of some SNRs.