The microwave permeability of composites made of ferrite particles in a non-magnetic matrix is a!ected by particle shape and size. To account for the second e!ect, we have developed a micromagnetic model for calculating the microwave polarizability of a particle with non-uniform magnetization. This model is described in detail: a generalized demagnetizing operator associated with the equilibrium magnetic configuration inside the particle is introduced; the polarizability is defined as the perturbation of this con"guration by the external magnetic excitation; the permeability of a macroscopic sample is calculated using a space averaging procedure. The numerical methods are introduced and results for two systems are discussed: domain modes in thin "lms and ferrite composites with planar anisotropy.