Patch robustness certification is an emerging kind of defense technique against adversarial patch attacks with provable guarantees. There are two research lines: certified recovery and certified detection. They aim to label malicious samples with provable guarantees correctly and issue warnings for malicious samples predicted to non-benign labels with provable guarantees, respectively. However, existing certified detection defenders suffer from protecting labels subject to manipulation, and existing certified recovery defenders cannot systematically warn samples about their labels. A certified defense that simultaneously offers robust labels and systematic warning protection against patch attacks is desirable. This paper proposes a novel certified defense technique called CrossCert. CrossCert formulates a novel approach by cross-checking two certified recovery defenders to provide unwavering certification and detection certification. Unwavering certification ensures that a certified sample, when subjected to a patched perturbation, will always be returned with a benign label without triggering any warnings with a provable guarantee. To our knowledge, CrossCert is the first certified detection technique to offer this guarantee. Our experiments show that, with a slightly lower performance than ViP and comparable performance with PatchCensor in terms of detection certification, CrossCert certifies a significant proportion of samples with the guarantee of unwavering certification.