Complementary Label Learning (CL) addresses the challenging weakly-supervised scenario where each training instance is annotated with a label indicating a class it does not belong to. Existing CL methods often rely on static or overly simplistic assumptions about the relationship between complementary labels and true underlying labels, and typically neglect the inherent uncertainty in inferring true labels from such indirect supervision. This paper introduces Meta-Complementary Label Uncertainty-Quantification and Calibration (MCL-UC), a novel algorithmic component designed to enhance CL performance. MCL-UC employs a lightweight Meta-Calibration Network (MCN) that learns to map an instance and its complementary label to the parameters of a Dirichlet distribution over the true class probabilities. This explicitly models the instance-specific uncertainty of the label inference. The MCN is trained on a small, clean validation set using a principled evidential loss. The uncertainty-quantified pseudo-labels generated by the MCN then guide the training of a main classifier in a robust manner, by down-weighting samples with high inferred label uncertainty. MCL-UC provides a dynamic, feature-aware, and uncertainty-cognizant mechanism for label correction in CL, offering a theoretically sound and efficient means to significantly improve upon traditional strategies.