Remote teleoperation of advanced, semi-autonomous robotic technologies has great potential in many industries critical to the economy and for the environment of the Middle East. Applications include maintenance of under-water oil wells, maintenance of nuclear power plants, counter-terrorism and national defense, law enforcement, remote sensing, and health care. In each of these applications, a user, likely without technology expertise, must operate a complex robot in uncertain and unknown environments. The nature of the tasks and environments encountered by the robot in these applications make it highly likely that the robot's limited autonomy will fail or be insufficient to complete the desired task. In this paper, we argue that, in such scenarios, cognitive telepresence, defined as the ability of the user to comprehend and control the robot's cognition, is an important design principle for human-robot systems. We compare and contrast cognitive telepresence to existing design principles commonly discussed in the literature, and define various metrics of cognitive telepresence. Finally, via two illustrative examples and a user study, we demonstrate the usefulness of cognitive telepresence as an important design principle of human-robot systems consisting of a user with limited technology expertise and a robot with limited and error-prone artificial intelligence.