Ammonia is made in a system that includes a conversion reactor for performing a Haber-Bosch process. Effluent streams from the conversion reactor, which include an ammonia component and excess hydrogen and nitrogen reactants, are fed to a membrane separator that includes NaA zeolite membranes disposed on one or more hollow porous supports. The NaA zeolite membranes are highly selective for the ammonia component, allowing the ammonia to be collected from a lumen of the membranes as a product and enriching the excess hydrogen and nitrogen reactants for reuse in the conversion reactor. These systems and the methods of their use are effective to replace and/or modify the energy-intensive condensation/recycling steps in the traditional Haber-Bosch process used to condense NH3 from the exiting stream of the reactor. The selective removal of ammonia by high quality NaA membranes helps to shift the ammonia evolution reaction.