When I was upgrading my WordPress 3.6.1 to 3.7 I came across below warning when trying to Upgrade Network:
Warning! Problem updating https://SITENAME. Your server may not be able to connect to sites running on it. Error message: SSL certificate problem: self signed certificate in certificate chain.
Luckily came across post from o6asan which put me on right track on fixing the issue. Basically in
wp-includes directory there is another directory
certificates which contains file
ca-bundle.crt. This file is simply a text file/library (in PEM format) containing public certificates of different CA(s), of course some of them are missing.
To work around my issue, since CAcert.org from which my certificates are was not included, I just added their root certificates (Class 1 PKI Key, Class 3 PKI Key) and was no loner seeing above warning.