Quantum transport is usually cast as an "open" scattering problem, for which available computational methods have not achieved the accuracy of methods for conventional "closed" problems. Here we cast quantum transport as a closed problem and demonstrate fully converged currents for the prototype benzene-dithiolate system. We further report results for carbon-nanotube field-effect transistors, highlighting differences with Si-based devices, e.g., band mixing caused by the gate electric field. We also find that the source-drain current exhibits an intrinsic saturation as a function of the gate voltage.