A real space renormalization group method for the percolation problem in isotropically and anisotropically correlated systems is proposed. The macroscopic conductive properties at all volume fractions of the conducting phase are computed. It is demonstrated that the anisotropy in the correlation structure of the original lattice has a major effect on its conductive properties. By comparison correlated isotropic lattices have effective conductive properties that differ only slightly from random lattices. Results are presented for binary conductance distributions and for three-and four-component lattices.