You can use the PrintingTools service to print maps that contain secure services using short-term tokens. However, printing maps that contain services secured with web-tier authentication is not supported.
If you use short-term tokens to secure services
If you secure your services using short-term tokens (the default), the user will be challenged to provide the name and password upon opening the web app. The token is then passed to the PrintingTools service when the user requests a map to be printed.
If you enforce security at the web server tier
Printing maps with the PrintingTools service is not supported if you enforce security at the web server tier.