We report the remarkably high electrical conductance of microporous 3D graphene-like carbons that were formed using lanthanum (La)-catalyzed synthesis in a Y zeolite (LaY) template investigated using conductive atomic force microscopy (C-AFM) and theoretical calculations. To uncover the relation between local electrical conductance and the microporous structures, we tuned the crystallographic ordering of LaY-templated carbon systems by changing the heating temperature. The structure of the LaY-templated carbon prepared at the higher temperature has graphene-like sp(2) hybridized bonds, which was confirmed using high-resolution transmission electron microscopy and X-ray diffraction measurements. C-AFM current-voltage spectroscopy revealed that the local current flow in the LaY-templated carbon depends on the quantity of C-C bonds within the narrow neck between the closed supercages (i.e. there are three types of carbon: carbon with heat treatment, carbon without heat treatment, and carbon synthesized at low temperature). The difference in electrical conductance on the LaY-templated carbon was also confirmed via theoretical computation using the Boltzmann transport theory and the deformation potential theory based on the density functional theory. These results suggest that the degree of order of the pores in the 3D zeolite-templated carbon structures is directly related to electrical conductance.