For the record, Gareth McCaughan is not the only person with this issue currently.
Recently, I've experienced exactly the same problem and, it appears to be, for exactly the same reason. In my case, the issuer of the certificate is "Huawei", the manufacturer of my fibre modem/router.
To be able to recover and allow Evernote to sync without this problem, I needed to exit from the Evernote desktop client and reboot the computer.
Also worth noting:
- Evernote is the only application that has this problem (including an application I've developed myself that syncs with OneNote).
- I'm running the desktop client build 220.127.116.1120 (304720) Public, under Windows 10.
- I agree with Gareth McCaughan that the Evernote client could have handled this issue a lot better, by, as he suggests, having the error provoke some sort of try-again-from-scratch response from Evernote.
- @gazumped Thanks for your interest and your useful comments.