Local critical current densities J c of large melt-textured YBa 2Cu 3O 7 and SmBa 2Cu 3O 7 samples were nondestructively measured using a previously developed ac inductive technique [Appl. Phys. Lett. 83 (2003) 3972]. In this method an ac magnetic field is generated by an ac drive current ( I 0cos ωt) in a small flat coil placed just above the superconductor, and a third-harmonic voltage ( V 3cos3 ωt) generated in the same coil due to the nonlinear magnetic response of type-II superconductors is measured. Because V 3 is proportional to I 0 2 and inversely proportional to J c, J c can be measured in the surface region (typically down to ∼0.1 mm beneath the surface) of the bulk superconductor by measuring V 3 as a function of I 0. The magnetic-field dependence of J c agreed reasonably well with that measured by using dc magnetization, if the effect of induced electric fields on J c is taken into account. By this ac inductive method J c can be measured by electric-field criteria ( E c≈10 −4–10 −2 V/m) that are higher than those generally used in transport measurements of J c ( E c=10 −4 V/m). We can measure the distribution of J c in a large superconducting sample by scanning the measuring coil over the entire sample surface.