In meta-heuristic optimisation, the robustness of a particular solution can be confirmed by re-sampling, which is reliable but computationally expensive, or by reusing neighbourhood solutions, which is cheap but unreliable. This work proposes a novel metric called the confidence measure to increase the reliability of the latter method, defines new confidence-based operators for robust meta-heuristics, and establishes a new robust optimisation approach called confidence-based robust optimisation. The confidence metric and five confidence-based operators are proposed and employed to design two new meta-heuristics: confidence-based robust Particle Swarm Optimisation and confidence-based robust Genetic Algorithm. A set of fifteen robust benchmark problems is employed to investigate the efficiencies of the proposed algorithms. The results show that the proposed metric is able to calculate the confidence level of solutions effectively during the optimisation process. In addition, the results demonstrate that the proposed operators can be employed to design a confident robust optimisation process and are readily applicable to different meta-heuristics.