The tortuosity (tau), defined in the present context as the ratio of the free diffusion coefficient to the restricted diffusion coefficient of a contained fluid, is an important but difficult to measure characteristic of a porous medium, particularly when it is partially saturated with water. We develop and apply methodology, based on nuclear magnetic resonance (NMR) pulsed field gradient techniques, to measure tau for various sandstone rock cores as a function of residual water fraction. The NMR methodology requires the use of bipolar pulsed field gradient stimulated echo pulse sequences to avoid systematic errors due to magnetic susceptibility differences and D2O as a stationary immiscible water phase; this was selected as it provides no H-1 NMR signal. Tortuosity of the free pore space was successfully measured using liquid ethane as a probe fluid for three different sandstones over the full accessible range of residual water saturation. Generally, the tortuosity was observed to increase with residual water (D2O) content; however, significant variations were observed between the different sandstones.