Nuclear magnetic resonance (NMR) systems and methods employing squashed (transversely-elongated) sample vessels (sample tubes or flow cells) for holding liquid NMR samples, and matching squashed saddle-shaped RF coils allow reducing sample and/or coil losses and increasing the RF circuit quality factors (Q). In a present implementation, the RF coils and sample vessels have rectangular cross-sections. Rounded (e.g. ellipsoidal) or other squashed cross-sections may also be used. The coil corresponding to the highest sample losses is positioned such that the magnetic field generated by the coil is along the major axis of the sample vessel. Squashed sample vessels may also be used with conventional circular coils, particularly for low-temperature measurements where sample losses dominate.