I am using MAMP Pro 1.9.4 on Mac OSX In phpinfo() I see curl is enabled
phpinfo()
cURL support enabled cURL Information 7.20.0 Age 3 Features
In MAMP, if you are getting errors when connecting to HTTPS hosts, just set this option:
curl_setopt($ch, CURLOPT_SSLVERSION,3);
The equivalent by command line is:
curl -k -ssl3 https://www.your-secure-host.com