Using Twilio with Classic ASP and VBScript enables developers to initiate calls and send text messages using the REST API. By making a simple POST request, developers can place a call via the REST API, specifying parameters such as the caller's number, called party's number, and URL handler for the call. Similarly, sending an SMS is straightforward, requiring only a few lines of code to authenticate with Twilio and post the message parameters, including the sender's number, recipient's number, and message contents. The examples provided demonstrate how to use Twilio with Classic ASP and VBScript, offering a starting point for developers looking to integrate Twilio into their applications.