In this paper, we consider homogenization of the Landau-Lifshitz equation with a highly oscillatory material coefficient with period epsilon modeling a ferromagnetic composite. We derive equations for the homogenized solution to the problem and the corresponding correctors and obtain estimates for the difference between the exact and homogenized solution as well as corrected approximations to the solution. Convergence rates in epsilon over times O(epsilon(sigma)) with 0 <= sigma <= 2 are given in the Sobolev norm H-q, where q is limited by the regularity of the solution to the detailed Landau-Lifshitz equation and the homogenized equation. The rates depend on q, sigma and the number of correctors.