The shaping of magnetic fields is important in many areas ofphysics, including magnet shimming, electromagnetic traps, magneticdomain switching, and controlled spin precession in nuclear magneticresonance (NMR). We examine the method of target field matching byorthogonal projection and its application to NMR, whereby the phase ofnuclear spins in a strongly inhomogeneous field is corrected throughstroboscopic ac irradiation using matching fields. Three-dimensionalshaping of static and ac fields can restore the spectral resolution byorders of magnitude using simple linear combinations of a small number ofindependent sources. Results suggest the possibility of substantiallypushing the current limits of high-resolution NMR spectroscopy in weakand inhomogeneous fields. We also discuss conditions under whichconcomitant gradient effects are important in high magnetic fields andthe geometric-phase errors they introduce during precession in acfields.