In the current context of biometric system certification, it is essential to address inherent biases to ensure both fairness and accuracy. Our research introduces a new method for estimating biases in these systems, particularly under grey box conditions, which are commonly encountered in certification settings. We aim to quantify biases in gender and ethnicity using advanced metrics applied to a selected database that combines the datasets VGGFace, VGGFace2, and CWD. Our methodology implies the variation of decision thresholds to observe changes in metrics, thereby uncovering biases. The goal of this research is to compare metrics on their biases evaluation way. The outcomes are intended to aid in establishing a congruous protocol for bias estimation in biometric systems, thereby enhancing the fairness and dependability of biometric authentication methods.