Improving transport properties of electrolytes is important for developing lithium-ion batteries for future energy storage applications. In Newman's concentrated solution theory, electrolytes are characterized by three transport parameters, conductivity, diffusion coefficient, and transference number, in addition to the thermodynamic factor. In this work, these parameters are all determined for an exemplar liquid electrolyte, lithium bis(trifluoromethanesulfonyl)imide mixed in tetraethylene glycol dimethyl ether, using electrochemical methods. The intrinsic coupling between parameters obtained by electrochemical methods results in large error bars in the transference number that obscure the transport behavior of the electrolyte. Here, we use electrophoretic NMR (eNMR) to measure the electric-field-induced ion and solvent velocities to obtain the transference number directly, which enables determination of the thermodynamic factor with greater certainty. Our work indicates that the combination of eNMR and electrochemical methods provides a robust approach for complete characterization of battery electrolytes.