To implement secure authentication for Twilio requests in a Sinatra application, an Authentication Token must be set by exporting it as an environment variable or passing it through the Rack middleware. This token is used to validate incoming requests and ensure that they are genuine. The application can then use custom validation logic to determine whether to process the request or return an error response. To test this setup, a mocking library should be used in tests to avoid failures due to Twilio request validation.