Biological membranes contain a high concentration of mobile embedded proteins. While the Brownian motion of single membrane proteins has been studied in detail, the dynamic correlations between proteins have received little attention. We account for the correlated motion of proteins in a membrane, which is either free in solution or lying at a finite distance from a rigid surface. The effect of protein concentration on the correlated motion and on the response of the membrane to stresses is studies as well. We find qualitative differences in the dynamics of membrane proteins between the case of a free membrane and that of a supported one. These differences arise from the fact that the former system conserves momentum whereas the latter does not.