A growing body of literature shows that the transverse relaxation times of the placenta change during pregnancy and may be an early indicator of disease. Magnetic resonance imaging (MRI) of pregnant women is not, however, currently used frequently despite this evidence. One significant barrier to adoption is the cost of undertaking an MRI scan and the over utilization of existing equipment. Low-field nuclear magnetic resonance (NMR) offers a low-cost alternative, capable of measuring transverse relaxation in a single point in space. Ultrasound imaging (US) is routinely used at several points during pregnancy but is not capable of early detection of pre-eclampsia, for example. It does, however, provide a technique that is capable of locating the placenta with ease. In combination with a single point low-field measurement, localised with ultrasound imaging allows access to this exciting technique without the need for an expensive traditional MRI. In this work, we present a unilateral system (NMR CAPIBarA), operating at a magnetic field of only 18mT, which measures transverse relaxation times at distances from its surface equivalent to the positioning of a human placenta. Data are presented to characterise the system using relation time standards covering the full transverse relaxation time range relevant for the developing placenta, which are also measured on a 1.5 T clinical MRI scanner.