We have studied the implications of high-sensitivity polarization measurements of objects from the Wilkinson Microwave Anisotropy Probe (WMAP) point source catalogue made using the Very Large Array (VLA) at 8.4, 22 and 43 GHz. The fractional polarization of sources is almost independent of frequency with a median of ≈2 per cent and an average, for detected sources, of ≈3.5 per cent. These values are also independent of the total intensity over the narrow range of intensity we sample. Using a contemporaneous sample of 105 sources detected at all three VLA frequencies, we have investigated the spectral behaviour as a function of frequency by means of a two-colour diagram. Most sources have power-law spectra in total intensity, as expected. On the other hand, they appear to be almost randomly distributed in the polarized intensity two-colour diagram. This is compatible with the polarized spectra being much less smooth than those in intensity and we speculate on the physical origins of this. We have performed an analysis of the correlations between the fractional polarization and spectral indices including computation of the principal components. We find that there is little correlation between the fractional polarization and the intensity spectral indices. This is also the case when we include polarization measurements at 1.4 GHz from the NRAO VLA Sky Survey (NVSS). In addition we compute 45 rotation measures from polarization position angles which are compatible with a λ2 law. We use our results to predict the level of point source confusion noise that contaminates cosmic microwave background polarization measurements aimed at detecting primordial gravitational waves from inflation. We conclude that some level of source subtraction will be necessary to detect r∼ 0.1 below 100 GHz and at all frequencies to detect r∼ 0.01. We present estimates of the level of contamination expected and the number of sources which need to be subtracted as a function of the imposed cut flux density and frequency.