Using superconducting magnetic Wollaston prisms, high-resolution neutron Larmor diffraction has been implemented at the High-Flux Isotope Reactor of Oak Ridge National Laboratory (ORNL), Tennesse, USA. This technique allows the inverse relationship between the achievable diffraction resolution and the usable neutron flux to be overcome. Instead of employing physically tilted radio-frequency spin flippers, the method uses magnetic Wollaston prisms which are electromagnetically tuned by changing the field configurations in the device. As implemented, this method can be used to measure lattice-spacing changes induced, for example, by thermal expansion or strain with a resolution of Δd/d ≃ 10−6, and the splitting of sharp Bragg peaks with a resolution of Δd/d = 3 × 10−4. The resolution for discerning a change in the profile of a Bragg peak is Δd/d < 10−5. This is a remarkable degree of precision for a neutron diffractometer as compact as the one used in this implementation. Higher precision could be obtained by implementing this technique in an instrument with a larger footprint. The availability of this technique will provide an alternative when standard neutron diffraction methods fail and will greatly benefit the scientific communities that require high-resolution diffraction measurements.