A combustor (20) for a gas turbine engine (10) is disclosed. The combustor (20) is described as comprising a dome plate (25) coupled to a liner thereof, with at least one heat shield (26) comprised of a ceramic matrix composite coupled at the aft end of the dome plate (25). Also described is a method for assembling a combustor (20) for a gas turbine engine (10), including releasing a metal alloy heat shield from a dome plate (25) and providing a ceramic matrix composite heat shield (26) as replacement.