Cyber threats against space infrastructures, including satellites and systems on the ground, have not been adequately understood. Testbeds are important to deepen our understanding and validate space cybersecurity studies. The state of the art is that there are very few studies on building testbeds, and there are few characterizations of testbeds. In this paper, we propose a framework for characterizing the fidelity of space cybersecurity testbeds. The framework includes 7 attributes for characterizing the system models, threat models, and defenses that can be accommodated by a testbed. We use the framework to guide us in building and characterizing a concrete testbed we have implemented, which includes space, ground, user, and link segments. In particular, we show how the testbed can accommodate some space cyber attack scenarios that have occurred in the real world, and discuss future research directions.