A method to identify the law of roll motion decay from extreme angles is presented based on perturbations of the elliptic-type solutions of the corresponding Hamiltonian system. Restoring polynomials up to the 7th order are considered. It is shown that the decay law can be expressed in closed form for up to quintic restoring. The method should be especially useful for deriving linear and nonlinear roll damping coefficients in the context of ship capsize investigations where the large amplitude behavior, near to the angle of vanishing stability, needs to be taken into account.