In this paper, we propose a reference governor-based approach to guarantee enforcement of critical flight constraints on the Altaeros tethered, lighter-than-air wind energy system. While the high-altitude flight made available by the tethered system leads to significant increases in power production over traditional, tower-mounted systems, the freedom of motion resulting from the tethers and aerodynamic shell introduces critical attitude and tether tension constraints. To date, methods considered for enforcing these constraints have relied upon heuristic static maps or model predictive control (MPC). The former cannot guarantee transient constraint satisfaction, whereas the latter is computationally burdensome given Altaeros's current microcontroller capabilities. The approach pursued in this paper uses a reference governor, which is a computationally simple add-on to the existing controller that enforces transient and steady-state constraints. The methodology proposed in this paper is demonstrated through simulations on linear and nonlinear models of the longitudinal dynamics of the Altaeros system with wind gust disturbances.