A combustor includes an end cap having a perforated downstream plate and a combustion chamber downstream of the downstream plate. A plenum is in fluid communication with the downstream plate and supplies a cooling medium to the combustion chamber through the perforations in the downstream plate. A method for cooling a combustor includes flowing a cooling medium into a combustor end cap and impinging the cooling medium on a downstream plate in the combustor end cap. The method further includes flowing the cooling medium into a combustion chamber through perforations in the downstream plate.