If the customer is looking to synthetically test their site via a mobile device, this can be done via the synthetic monitor settings where a device profile can be set, screen orientation as well as bandwidth.
If you're just testing the mobile version of a web browser application Chad's answer will work. If you want to test a native mobile application (e.g. iOS, Android) you can look at using HTTP monitors and testing the API backends that the mobile apps make use of.
Multi-step HTTP monitors can help you to test workflows (e.g. get token, hit a service, etc...).