Are there any? What are their names? Are they publicly available/downloadable/installable?
The OKL4 Verified microkernel has passed the most stringent of Common Criteria evaluation assurance levels (EAL 7). Even this doesn't mean that it's "secure", "100% secure" or "more secure", it just means that it has been formally proved that the microkernel's implementation is compatible with the security model defined by the vendor.
Such a security model will contain assumptions about the environment and mode of operation of the software that may not be consistent with your environment. Taking a different example, when the Target of Evaluation is a commercial operating system the model usually assumes that all of the operators are benign and that any remote system to which the evaluated device is connected will also be consistent with the security model of the ToE.