A robotic telescope is both a complex system with many potential modes of failure, and an attractive target for computer criminals. The paper describes a systematic approach to security designed to optimize the operational continuity of such a system. This includes the development of policy guidelines, techniques for identifying the prioritizing the assets to be protected, and for assessing the threats against these assets. Commonly encountered threats are discussed, and specific security mechanisms to counter these threats described, including fault-tolerant hardware configurations, cryptographic techniques for authentication and confidentiality, and leveraging the properties of point-to-point wide-area networking links. A typical remote telescope offers multiple points of attack through its interfaces for engineering control, observation scheduling, data retrieval and routine management. A case study is presented highlighting the engineering trade-offs required to protect these interfaces, and discussing the implementation of specific countermeasures described earlier. Finally some recommendations are made for managing the human aspects of security implementations.