I have been asking the same question for over a month now. Neither Edge nor IE11 (I know! But I had to try) opens several HTTPS pages, including my institution's mailserver. The error message on Edge is the dreaded:
Can’t connect securely to this page
This might be because the site uses outdated or unsafe TLS security settings.
If this keeps happening, try contacting the website’s owner.
Your TLS security settings aren’t set to the defaults, which could also be causing this error
The error message on IE11 is slightly different, but points to pretty much the same end result.
Firefox (54.0.1 32-bit) and Chrome (59.0.3071.115 64-bit) both open these HTTPS pages just fine.
I have tried all the options I found on the net. Clearing SSL cache, resetting internet options to default, re-registering dlls, enabling/disabling SSL 2, 3, and TLS 1 (TLS 1.1 and 1.2 are always enabled) - all to no avail.
My windows version is 1703 (OS build 15063.483) 64-bit.
Not using any external antivirus other than Windows Defender in Windows 10. No external firewall either. I'm connected to the institutional network directly via LAN. No proxies.
Can someone please help? Anyone has any answers, advice, opinions? Please share. Thanks in advance.
UPDATE 1: I have established that if TLS1.0 is checked, the "Your TLS security settings aren’t set to the defaults, which could also be causing this error" part of the error message goes away. The problem of not connecting to HTTPS sites remains though.
UPDATE 2: Additional weirdness. Within my institution's HTTPS websites, not all are unreachable from Edge/IE. One specific TLD, j***s.edu (which hosts the mailserver), seems to be giving the problem. Edge/IE11 is unable to get to:
either https://login.j***s.edu (which is the landing point for all the institutional resources via a SSO mechanism)
or https://mobile.j***s.edu (which is the path to the mailserver and Outlook Web Access)
If I ping either of these sites from my computer using a CMD prompt, the ping works quite well and I see the corresponding IP address, too. So this appears not to be a DNS-related issue.
To reiterate, I can reach https://mobile.j***s.edu/owa from Chrome/Firefox, but not Edge/IE11. The mailserver path is correct, too, because this is the path used to configure Outlook 2016 on my Windows 10 Pro 64-bit Laptop as well as the iOS Outlook mail app. It only doesn't seem to work from my Desktop.
UPDATE 3: I reimaged Windows 10 Pro x64 (v1703 = same as mine) on a colleague's laptop, and installed Outlook 2016 and other Office programs via Office 365 institutional subscription (= same as mine). In that laptop, Edge can reach the same website https://mobile.j***s.edu/owa with NO ISSUE, and I could configure Outlook 2016 to reach the institutional mailserver via Exchange with NO ISSUE either. So, the problem may be peculiar to how my Desktop machine handled the Creator's Update.
UPDATE 4 (FINAL): I took the extreme step, and reset my Windows 10 installation with the 'Keep my files' option. The process re-installed Windows and everything in it, including Edge. It was painful, because I had to manually reinstall all my software programs, including Office 2016, but at the end of it, EVERYTHING WORKS now. Edge connects to all websites it was previously unable to, Microsoft Outlook has no problem connecting to my institution's Exchange Server, and even the LONG-STANDING issue of the Xbox app on Windows 10 not recognizing my login and password has been resolved.