Abstract: We use a sample of Swift and Fermi short gamma-ray bursts (SGRBs) to test the validity of the Amati and Yonetoku correlations, which were originally found for long bursts. The first relation is between Ep,i , the intrinsic peak energy of the GRB prompt emission, and Eiso, the equivalent isotropic energy. The second relationship is between Ep,i and Liso, the peak isotropic luminosity. The sample is composed of 36 Swift SGRBs and 15 Fermi SGRBs that have measured redshifts and whose spectral parameters, with their uncertainties, are available online. The uncertainties (error bars) on the values of the calculated energy flux P, of the energy Eiso, and of the peak isotropic luminosity peak Liso are estimated using a Monte Carlo approach. We find that SGRB energy and luminosity quantities (Ep,i , Liso, and Eiso) can be correlated with Amati- and Yonetokulike relations reasonably well (Pearson r-values of 0.5 and 0.6, respectively), although the data shows large scatter and hence large error bars on the slope and the intercept of the fitting line. Our results are consistent with other similar works, though we here use the largest sample of SGRBs with redshifts so far on this topic. We also find that Eiso and Liso seem to evolve with redshift as (1+z)4.9±0.3 and (1+z)5.5±0.9, respectively, with a moderate goodness of fit. However, we caution that this is probably due to selection effects rather than being a genuine redshift evolution of Eiso and Liso.