There has been much publicity surrounding the use of machine learning technologies in self-driving cars and the challenges this presents for guaranteeing safety. These technologies are also being investigated for use in manned and unmanned aircraft. However, systems that include learning-enabled components (LECs) and their software implementations are not amenable to verification and certification using current methods. We have produced a demonstration of a run-time assurance architecture based on a neural network aircraft taxiing application that shows how several advanced technologies could be used to ensure safe operation. The demonstration system includes a safety architecture based on the ASTM F3269-17 standard for bounded behavior of complex systems, diverse run-time monitors of system safety, and formal synthesis of critical high-assurance components. The enhanced system demonstrates the ability of the run-time assurance architecture to maintain system safety in the presence of defects in the underlying LEC.