Ok, so found a couple of things for anyone else having this problem. Tried using CURLOPT_SSL_VERIFYPEER set to false, just to try to force the request - it's not a good idea to use in production as it ignores verification of the cert. However, this was still not working. var_dump on the request shows FALSE. By echoing out the curl_error() function, I got the following message which will help lead to the solution - it gives

"SSL: no alternative certificate subject name matches target host name 'www.myapi.com'"

So I'm following this route now - may be that I need to provide Laravel/PHP Curl with a link to a local copy of my cert... I'll post anything new I find.

So, for the moment leaving peer and host checking set to false allows me to get my data. I need to investigate why my SSL cert is giving conflicting information about its identity, but for the moment, this will work:

$ch=curl_init();
curl_setopt($ch, CURLOPT_URL, $url);
curl_setopt($ch, CURLOPT_VERBOSE, true);
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
curl_setopt($ch, CURLOPT_SSL_VERIFYHOST, false); // <-- This turns off host verification
curl_setopt($ch, CURLOPT_SSL_VERIFYPEER, false); // <-- And this turns off ssl verification
$output = curl_exec($ch);
return $output;

I'll post a fuller explanation when I've found one :-)

Wittner