Adversarial perturbation is a severe threat to deep learning-based systems such as classification and recognition because it makes the system output wrong answers. Designing robust systems against adversarial perturbation in a \textit{certifiable} manner is important, especially for security-related systems such as face recognition. However, most studies for certifiable robustness are about classifiers, which have quite different characteristics from recognition systems for verification; the former is used in the closed-set scenario, whereas the latter is used in the open-set scenario. In this study, we show that, similar to the image classifications, 1-Lipschitz condition is sufficient for certifiable robustness of the face recognition system. Furthermore, for the given pair of facial images, we derive the upper bound of adversarial perturbation where the 1-Lipschitz face recognition system remains robust. At last, we find that this theoretical result should be carefully applied in practice; Applying a training method to typical face recognition systems results in a very small upper bound for adversarial perturbation. We address this by proposing an alternative training method to attain a certifiably robust face recognition system with large upper bounds. All these theoretical results are supported by experiments on proof-of-concept implementation. We released our source to facilitate further study, which is available at \textcolor{red}{github}.