We describe a novel Godunov-type numerical method for solving the equations\nof resistive relativistic magnetohydrodynamics. In the proposed approach, the\nspatial components of both magnetic and electric fields are located at zone\ninterfaces and are evolved using the constrained transport formalism. Direct\napplication of Stokes' theorem to Faraday's and Ampere's laws ensures that the\nresulting discretization is divergence-free for the magnetic field and\ncharge-conserving for the electric field. Hydrodynamic v…