Safari reports it can't establish a secure connection to the server
This began yesterday, May 30, on several sites, all of which are large organizations that have valid certificates. All of these sites open correctly on Chrome, Firefox and Opera. One of the sites is my web host which provides my email; Apple Mail reported a similar problem with an invalid certificate for my email addresses. While I could work around the problem with my email by telling Mail to trust the certificate, that doesn't solve the basic problem of Safari and Mail reporting valid certificates to be invalid. I am using the latest OS available for my early 2009 iMac, OS 10.11.6, which uses Safari 11.1.2. Any help would be much appreciated.
iMac, OS X 10.11