This paper presents a minimal validated framework for designing energy-aware metaheuristics that operate under fixed energy budgets. We introduce a unified operator-level model that quantifies both numerical gain and energy consumption, and define a robust Expected Improvement per Joule (EI/J) score to guide adaptive selection among operator variants during the search. The resulting energy-aware solvers dynamically choose between operators to self-control exploration and exploitation, aiming to maximise fitness gain under limited energy. We instantiate this framework in three representative metaheuristics—steady-state GA, PSO, and ILS—each equipped with two lightweight/heavy update variants in a controlled setting. Experiments on three heterogeneous combinatorial problems (Knapsack, NK-landscapes, and Error-Correcting Codes) show that the energy-aware variants can reach comparable fitness while requiring substantially less energy than their non-energy-aware baselines. EI/J values stabilise early and yield clear operator-selection patterns, with each solver reliably self-identifying the most improvement-per-Joule-efficient operator across problems.