The TUCAN EDM experiment aims to measure the neutron electric dipole moment (EDM) to a precision of cm. The experiment is a precise relative measurement of the spin precession frequency of ultracold neutrons stored in a bottle, placed in homogenous magnetic and electric fields. The magnetic field is shielded from external influences by conducting the experiment in a magnetically shielded room (MSR). A main precession field of T is produced by an internal coil. Magnetic field inhomogeneity in the coil/MSR system will cause the neutron spins to dephase as they precess, reducing the statistical precision of the experiment. Controlling the homogeneity is also important for false EDM signals. A system of square shim coils, mounted on the surface of a cube surrounding the experiment, is being developed to make adjustments to the field. This presentation will discuss quantitatively the magnetic homogeneity requirements, and demonstrate the ability of the shim coil design to meet them.