The exploitation of publicly accessible data has led to escalating concerns regarding data privacy and intellectual property (IP) breaches in the age of artificial intelligence. To safeguard both data privacy and IP-related domain knowledge, efforts have been undertaken to render shared data unlearnable for unauthorized models in the wild. Existing methods apply empirically optimized perturbations to the data in the hope of disrupting the correlation between the inputs and the corresponding labels such that the data samples are converted into Unlearnable Examples (UEs). Nevertheless, the absence of mechanisms to verify the robustness of UEs against uncertainty in unauthorized models and their training procedures engenders several under-explored challenges. First, it is hard to quantify the unlearnability of UEs against unauthorized adversaries from different runs of training, leaving the soundness of the defense in obscurity. Particularly, as a prevailing evaluation metric, empirical test accuracy faces generalization errors and may not plausibly represent the quality of UEs. This also leaves room for attackers, as there is no rigid guarantee of the maximal test accuracy achievable by attackers. Furthermore, we find that a simple recovery attack can restore the clean-task performance of the classifiers trained on UEs by slightly perturbing the learned weights. To mitigate the aforementioned problems, in this paper, we propose a mechanism for certifying the so-called $(q, η)$-Learnability of an unlearnable dataset via parametric smoothing. A lower certified $(q, η)$-Learnability indicates a more robust and effective protection over the dataset. Concretely, we 1) improve the tightness of certified $(q, η)$-Learnability and 2) design Provably Unlearnable Examples (PUEs) which have reduced $(q, η)$-Learnability.