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The dynamic voltage and frequency scaling (DVFS) technique is the basis of numerous state-of-the-art energy management schemes proposed for real-time embedded systems. However, recent research has illustrated the alarmingly negative impact of DVFS on task and system reliability. In this paper, we consider the problem of assigning processing frequencies to a set of real-time tasks in order to maximize the overall reliability, under given time and energy constraints. First, under the frame-based task model, we formulate the problem as a nonlinear optimization problem and show how to obtain the static optimal solution. Then, we propose online (dynamic) algorithms that detect early completions and adjust the task frequencies at runtime, to improve overall reliability. Furthermore, we extend these solutions to the periodic task model, with both static and dynamic solutions. All our solutions ensure that all timing constraints are met while the cumulative energy consumption of tasks does not exceed the given energy budget. Our simulation results indicate that our algorithms perform comparably to a clairvoyant optimal scheduler that knows the exact workload in advance.