SSL Safari can’t establish a secure connection to the server

Run the impacted domain site through SSLLabs SSL tester for clues SSL Server Test (Powered by Qualys SSL Labs)

 

Click on one of those listed IPs for actual results

But for my blog interesting. What version of Safari? Device used?

 

Is this on same device or different devices? Cloudflare forums might have clues

Do you have Cloudflare minimum TLS version set to 1.2? That might be why but I have that set on centminmod.com, community.centminmod.com and blog.centminmod.com, so you should have same problems on all 3 domains. Only difference is on blog.centminmod.com and centminmod.com I use Cloudflare SSL certificates provided by Google Trust SSL CA and with community.centminmod.com I am still using older Digicert SSL CA certificate

However from SSLLab tests there's link to expand Not simulated clients due to protocol mismatch and Safari 5 and 6 are listed due to SSL ciphers on those devices not supporting the ones Cloudflare edge servers are advertising as supported. Meaning your device is too old for Cloudflare's default strong SSL cipher supported methods.



You can try paying an extra $10/month for Cloudflare Advanced Certificate Management Advanced certificates · Cloudflare SSL/TLS docs and then using ACM product features Manage advanced certificates · Cloudflare SSL/TLS docs modify the default Cloudflare supported SSL ciphers Manage advanced certificates · Cloudflare SSL/TLS docs and Customize cipher suites — Edge certificates · Cloudflare SSL/TLS docs. Though that will only help temporarily if not at all depending on how old the device is. Eventually, older devices just need to be retired or upgraded.

Safari 5/6 probably looking for TLS 1.0/1.1 which have been deprecated and unsupported on a lot of web browsers/operating systems and services now. So I'd update your device.

Here's Cloudflare's default SSL ciphers Supported cipher suites — Edge certificates · Cloudflare SSL/TLS docs. On my centminmod domain sites I use ACM to disable weak SSL ciphers so older devices aren't supported as you can see in below SSLLabs protocol and SSL ciphers supported at Cloudflare edge