Amazon API Gateway is an essential tool for developing microservices-based architectures, thanks to its ability to efficiently manage multiple API endpoints and facilitate communication between decoupled services. It provides an abstraction layer that allows developers to expose specific service functionalities through RESTful or WebSocket APIs without having to manage the complexity of the underlying infrastructure. This allows each microservice to be developed, deployed, and scaled independently, enhancing development agility and making it easier to implement updates or new features without impacting other services. API Gateway also supports authentication and authorization, request validation, and traffic monitoring, which are critical for maintaining integrity and security in a microservices architecture.