Summary: In a thin-film ferromagnet, the leading-order behaviour of the magnetostatic energy is a strong shape anisotropy, penalizing the out-of-plane component of the magnetization distribution. We study the thin-film limit of Landau-Lifshitz-Gilbert dynamics, when the magnetostatic term is replaced by this local approximation. The limiting two-dimensional effective equation is overdamped, i.e. it has no precession term. Moreover, if the damping coefficient of three-dimensional micromagnetics is \(a\), then the damping coefficient of the two-dimensional effective equation is \(a + 1/a\); thus reducing the damping in three dimensions can actually increase the damping of the effective equation. This result was previously shown by García-Cervera and E using asymptotic analysis; our contribution is a mathematically rigorous justification.