We present follow-up observations of 97 point sources from the Wilkinson Microwave Anisotropy Probe (WMAP) 3-yr data, contained within the New Extragalactic WMAP Point Source catalogue between -4° <= δ <= 60° the sources form a flux-density-limited sample complete to 1.1Jy (~5σ) at 33GHz. Our observations were made at 16GHz using the Arcminute Microkelvin Imager and at 33GHz with the Very Small Array (VSA). 94 of the sources have reliable, simultaneous - typically a few minutes apart - observations with both telescopes. The spectra between 13.9 and 33.75GHz are very different from those of bright sources at low frequency: 44 per cent have rising spectra (α33.7513.9 < 0.0), where S ~ ν-α, and 93 per cent have spectra with α33.7513.9 < 0.5; the median spectral index is 0.04. For the brighter sources, the agreement between VSA and WMAP 33-GHz flux densities averaged over sources is very good. However, for the fainter sources, the VSA tends to measure lower values for the flux densities than WMAP. We suggest that the main cause of this effect is the Eddington bias arising from variability. We kindly request that any reference to this paper cites `AMI Consortium: Davies et al. 2009'. Issuing author - email: m.davies [at] mrao.cam.ac.uk (m[dot]davies[at]mrao[dot]cam[dot]ac[dot]uk) ‡ E-mail: t.franzen [at] mrao.cam.ac.uk (t[dot]franzen[at]mrao[dot]cam[dot]ac[dot]uk)