Ok, Opera Mini works and another alternative (UCBrowser) works too with https: sites.

UCBrowser for Symbian S60 v9.2.0.336 S60V3 date: 2013-10-15

I submitted an official bug report to https://bugs.opera.com/wizard/mobile

Browser: Opera Mobile for Symbian 12.00 (2258), phone Nokia C5-00 (browser info: Last updated(?) 2011

Browser which works with https: sites (Opera Mini for Symbian 7.1), browser info: Last updated(?) 2012

Tried older version Opera Mobile v11.50 but no difference, ssl-sites don't seem to open.

http://phoneky.com/applications/?id=y1y36596

Obviously this Opera Mobile 12 for Symbian needs an update.

This is strange, Opera Mini for Symbian opens https: sites okay in Nokia C5-00.

But the Opera Mobile 12 browser rejects the https connections.