Polarization and total power at 5000 MHz and 2700 MHz have been obtained for 30 supernova remnants (SNR) using the 64-m radio telescope at Parkes. This large sample includes a range of SNR from the young bright objects (such as Kepler's SNR) through the old faint sources such as MSH 14-63. Among the old remnants, the individual SNR have very varied properties, but several general conclusions emerge from our study. (1) In many cases, the polarization of the galactic background is as strong as that of the SNR and can vary significantly over the angular extent of the SNR. (2) The Faraday rotation is generally small and varies quite uniformly across the source. (3) The magnetic field patterns, although associated with the SNR, do not show any particularly characteristic pattern or relations to the total-power structure of the source.