Dynamic voltage and frequency scaling (DVFS) has been widely used to manage energy in real-time embedded systems. However, it was recently shown that DVFS has direct and adverse effects on system reliability. In this work, we investigate static and dynamic reliability-aware energy management schemes to minimize energy consumption for periodic real-time systems while preserving system reliability. Focusing on earliest deadline first (EDF) scheduling, we first show that the static version of the problem is NP-hard and propose two task-level utilization-based heuristics. Then, we develop a job-level online scheme by building on the idea of wrapper-tasks, to monitor and manage dynamic slack efficiently in reliability-aware settings. The feasibility of the dynamic scheme is formally proved. Finally, we present two integrated approaches to reclaim both static and dynamic slack at runtime. To preserve system reliability, the proposed schemes incorporate recovery tasks/jobs into the schedule as needed, while still using the remaining slack for energy savings. The proposed schemes are evaluated through extensive simulations. The results confirm that all the proposed schemes can preserve the system reliability, while the ordinary (but reliability-ignorant) energy management schemes result in drastically decreased system reliability. For the static heuristics, the energy savings are close to what can be achieved by an optimal solution by a margin of 5 percent. By effectively exploiting the runtime slack, the dynamic schemes can achieve additional energy savings while preserving system reliability.