We have mapped linearly polarized dust emission from the prestellar cores L1498 and L1517B with the James Clerk Maxwell Telescope (JCMT) using the Submillimetre Common User Bolometer Array (SCUBA) and its polarimeter SCUBAPOL at a wavelength of 850um. We use these measurements to determine the plane-of-sky magnetic field orientation in the cores. In L1498 we see a magnetic field across the peak of the core that lies at an offset of 19 degrees to the short axis of the core. This is similar to the offsets seen in previous observations of prestellar cores. To the southeast of the peak, in the filamentary tail of the core, we see that the magnetic field has rotated to lie almost parallel to the long axis of the filament. We hypothesise that the field in the core may have decoupled from the field in the filament that connects the core to the rest of the cloud. We use the Chandrasekhar-Fermi (CF) method to measure the plane-of-sky field strength in the core of L1498 to be 10 +/- 7 uG. In L1517B we see a more gradual turn in the field direction from the northern part of the core to the south. This appears to follow a twist in the filament in which the core is buried, with the field staying at a roughly constant 25 degree offset to the short axis of the filament, also consistent with previous observations of prestellar cores. We again use the CF method and calculate the magnetic field strength in L1517B also to be 30 +/- 10 uG. Both cores appear to be roughly virialised. Comparison with our previous work on somewhat denser cores shows that, for the denser cores, thermal and non-thermal (including magnetic) support are approximately equal, while for the lower density cores studied here, thermal support dominates.< Réduire