We have made two different measurements of interfacial energies below 300 muK, at zero pressure and in magnetic fields up to 400 mT. A variable magnetic field profile allows us to stabilize and precisely manipulate the position of the A-B interface. First, we can derive the difference in wall wetting energies from the behaviour of the phase boundary as it enters and exits a stack of glass capillary tubes. Secondly, we can measure the surface tension from the level of over-or under-magnetization needed to force the interface through an aperture. These are the first surface energy measurements in high magnetic fields in the zero-temperature limit. Our results are in surprising agreement with earlier measurements at high pressure close to T-c.