We report on highly accurate femtosecond (fs) laser micromachining of a compound parabolic concentrator (CPC) fiber tip on a polymer optical fiber (POF). The accuracy is reflected in an unprecedented correspondence between the numerically predicted and experimentally found improvement in fluorescence pickup efficiency of a Förster resonance energy transfer-based POF glucose sensor. A Zemax model of the CPC-tipped sensor predicts an optimal improvement of a factor of 3.96 compared to the sensor with a plane-cut fiber tip. The fs laser micromachined CPC tip showed an increase of a factor of 3.5, which is only 11.6% from the predicted value. Earlier state-of-the-art fabrication of the CPC-shaped tip by fiber tapering was of so poor quality that the actual improvement was 43% lower than the predicted improvement of the ideal CPC shape.