There are different forms of uncertainty in satellite communications, including cognitive interferers, channel conditions, packet traffic, and spectrum occupancy of users across channels. In addition, delay (such as propagation delay observed over satellite links) increases spectrum uncertainty and makes spectrum sensing and spectrum access two challenging tasks. To address such challenges, this paper presents a regret minimization solution for primary user (PU) and secondary user (SU) spectrum access to satellite resources in the presence of cognitive interferers. This robust game theoretic solution supports hierarchical spectrum sharing and dynamic spectrum access over multiple channels. Users select channels for data transmission and perform power control to optimize individual utility functions that are random due to different forms of uncertainty. The proposed game engine based on regret minimization framework provides a low-complexity and fast solution compared with traditional game solutions based on expected utility maximization. Detailed numerical results evaluate throughput and delay of PUs and SUs in the presence of cognitive interferers and compare the robust game theory-enabled approach with two benchmark schemes (with and without knowledge on channel availability). To support controllable and repeatable test and evaluation with real radios, an emulation testbed is built with software-defined radios connected with a network channel emulator that generates channel, mobility, and interference effects for satellite communications. GNU Radio modules are developed for cognitive network functionalities and run on USRP N210 radios that represent SU, PU, interferer, and satellite nodes. Emulation tests validate the effectiveness of the proposed solution under real radio effects.