The design of an air‐cored electomagnetic coil system is a very specific problem because of one essential feature: every characteristic parameter of the field produced is mainly determined by the geometry of the current‐bearing conductors. Various methods are presented to overcome the mathematical and computational difficulty of homogeneity optimization. Linearization of the field equations allows solving them with a pocket calculator, with some significant design restrictions. Nonlinear resolution and full system simulation can be performed at a computer center or on a scientifically‐oriented microcomputer system, both possibilities having their own advantages and tradeoffs. As an example, the optimization of a whole‐body NMR imaging magnet is presented. Compensation of field inhomogeneities up to the 14thorder allows a drastic reduction of magnet size and power consumption. A sketch of the procedures and results at three different levels—pocket calculator, microcomputer, and computer center—is presented.