We present radial velocities for 38 low-mass candidate members of the {sigma} Orionis young group. We have measured their radial velocities by cross-correlation of high-resolution (R>>6000) AF2/Wide Field Fibre Optical Spectrograph (WYFFOS) spectra of the gravity-sensitive NaI doublet at 8183,8195{AA}, on the nights of 2003 January 3 and 4. The total sample contained 117 objects, of which 54 have sufficient signal-to-noise ratio to detect NaI at an equivalent width of 3{AA}; however, we only detect NaI in 38 of these. This implies that very low-mass members of this young group display weaker NaI absorption than similarly aged objects in the Upper Scorpius OB association. We develop a technique to assess membership using radial velocities with a range of uncertainties that does not bias the selection when large uncertainties are present. The resulting membership probabilities are used to assess the issue of exclusion in photometric selections, and we find that very few members are likely to be excluded by such techniques. We also assess the level of contamination in the expected pre-main-sequence region of colour-magnitude space brighter than I=17. We find that contamination by non-members in the expected pre-main-sequence region of the colour-magnitude diagram is small. We conclude that although radial velocity alone is insufficient to confirm membership, high signal-to-noise ratio observations of the NaI doublet provide the opportunity to use the strength of NaI absorption in concert with radial velocities to asses membership down to the lowest masses, where lithium absorption no longer distinguishes youth.