Safari can't open secure connection the server "XXXXXX"

[JOB]

I'm having the Imac 21,5, medio 2011, version OS X El Capitan 10.11.6, and since the beginning of October I have experienced that I cannot get in contact with homepages of companies, which haven't been a problem early.
I get the above mentioned message, and can't even pass by in any way. Anyone here who has experienced the same? Has it something to do with the new implementation here in Denmark with MITid?
Hope somebody can help with the problem, or a way to trespass.
Kind regard JOB

 

[TonyAguila]

Are you using Safari for web browsing? Apple has beefed up security throughout the system, not just web browsing. You may want to try connecting with another browser, e.g., Chrome, Firefox, MS Edge, Opera, etc. Download and install the ones you are comfortable using.

If you find one that is able to make the connection, but wish to stay with Safari as your primary browser, open Safari preferences and click on the Advanced tab. At the bottom of the window, click to activate “Show Develop menu in menu bar.”

The next time a page fails to load in Safari, pull down the Develop menu and under “Open Page With,” select the browser of your choice, the one that worked for you.

 

[Lufbrarunner]

Check the date and time is correct on your imac, in Safari you could also click Develop > Empty Caches.

I have similar problems on my 2008 imac, with Safari and Chrome on some sites, which both say there is a security certificate problem, other sites load with no problem

 

[maw_walker]

It could also be the root certificates for specific sites at not installed or at expired. These get updated during OS updates (typically) and perhaps older OS versions have outdated root certs. Just a guess.

 

[Lufbrarunner]

It could also be the root certificates for specific sites at not installed or at expired. These get updated during OS updates (typically) and perhaps older OS versions have outdated root certs. Just a guess.

That sounds plausible.