The identification and quantification of molecules in interstellar space and atmospheres of planets in the solar systems and in exoplanets rely on spectroscopic methods and laboratory work is essential to provide the community with the spectral features needed to analyse cosmological observations. Rotational spectroscopy in particular, with its intrinsic high resolution, allows the unambiguous identification of biomolecular building blocks and biosignature gases which can be correlated with the origin of life or the identification of habitable planets. We report the extension of the measured rotational transition frequencies of dimethylsulphoxide and its 34S and 13C isotopologues in the millimetre wave range (59.6–78.4 GHz) by use of an absorption spectrometer based on the supersonic expansion technique. Hyperfine patterns related to the methyl group internal rotation were analysed in the microwave range region (6–18 GHz) with a Pulsed Jet Fourier Transform spectrometer at extremely high resolution (2 kHz) and reliable predictions up to 116 GHz are provided. The focus on sulphur-bearing molecules is motivated by the fact that sulphur is largely involved in the intra- and inter-molecular hydrogen bonds in proteins and although it is the 10th most abundant element in the known Universe, understanding its chemistry is still a matter of debate. Moreover, sulphur-bearing molecules, in particular dimethylsulphoxide, have been indicated as possible biosignature gases to be monitored in the search of habitable exoplanets.