Context :

Aims : We study the spectral and polarization properties of supernova remnants ( SNRs ) based on our \lambda 6 cm survey data .

Methods : The observations were taken from the Sino-German \lambda 6 cm polarization survey of the Galactic plane .
By using the integrated flux densities at \lambda 6 cm together with measurements at other wavelengths from the literature we derive the global spectra of 50 SNRs .
In addition , we use the observations at \lambda 6 cm to present the polarization images of 24 SNRs .

Results : We derived integrated flux densities at \lambda 6 cm for 51 small SNRs with angular sizes less than 1 \degr .
Global radio spectral indices were obtained in all the cases except for Cas A .
For SNRs G15.1 - 1.6 , G16.2 - 2.7 , G16.4 - 0.5 , G17.4 - 2.3 , G17.8 - 2.6 , G20.4+0.1 , G36.6+2.6 , G43.9+1.6 , G53.6 - 2.2 , G55.7+3.4 , G59.8+1.2 , G68.6 - 1.2 , and G113.0+0.2 , the spectra have been significantly improved .
From our analysis we argue that the object G16.8 - 1.1 is probably an H II region instead of a SNR .
Cas A shows a secular decrease in total intensity , and we measured a flux density of 688 \pm 35 Jy at \lambda 6 cm between 2004 and 2008 .
Polarized emission from 25 SNRs were detected .
For G16.2 - 2.7 , G69.7+1.0 , G84.2 - 0.8 and G85.9 - 0.6 , the polarized emission is detected for the first time confirming them as SNRs .

Conclusions : High frequency observations of SNRs are rare but important to establish their spectra and trace them in polarization in particular towards the inner Galaxy where Faraday effects are important .