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When neural networks are confronted with unfamiliar data that deviate from their training set, this signifies a domain shift. While these networks output predictions on their inputs, they typically fail to account for their level of familiarity with these novel observations. This challenge becomes even more pronounced in resource-constrained settings, such as embedded systems or edge devices. To address such challenges, we aim to recalibrate a neural network's decision boundaries in relation to its cognizance of the data it observes, introducing an approach we coin as certainty distillation. While prevailing works navigate unsupervised domain adaptation (UDA) with the goal of curtailing model entropy, they unintentionally birth models that grapple with calibration inaccuracies - a dilemma we term the over-certainty phenomenon. In this paper, we probe the drawbacks of this traditional learning model. As a solution to the issue, we propose a UDA algorithm that not only augments accuracy but also assures model calibration, all while maintaining suitability for environments with limited computational resources.