This paper presents the development of a model for Nd:YAG laser ablation of cyclic olefin polymer (COP) films. Two Taguchi orthogonal array experimental designs were implemented to produce a model for the prediction of microchannel depth and width produced on ZeonorFilm® ZF14 and ZF16 polymer films via laser ablation. The width and depth of the produced microchannels were measured using 3D optical profilometry. Microchannels produced were seen to range in depth of up to 50 µm, and widths of 112 µm via single-pass laser depending on the grade of COP, with feature size increasing as the number of laser passes increased. The models are discussed in terms of adjusted coefficient of determination, signal to noise ratio and model significance. The effect of the process parameters used such as fluence and scan speed on three different grades of COP was examined with an aim to produce a simple model suitable for predictive control of surface microstructuring of COP.