A popular metaheuristic global optimization technique called Cuckoo Search Algorithm (CSA) is employed to design non-integer order integrators (NOIs) in terms of the Infinite Impulse Response (IIR) templates in this paper. Extensive comparisons on the basis of design quality robustness, error convergence, and optimization time of the CSA-based NOIs are carried out with the Particle Swarm Optimization (PSO) based designs. Results demonstrate the efficient performance of CSA in exploring the multimodal, non-linear, and non-uniform error surface for this optimization problem. The CSA-based designs also outperform the recent literature by 9.67 decibel (dB) and 19.26 dB in terms of mean absolute relative magnitude error (MARME) and maximum absolute magnitude error (MAME) metrics, respectively.