Based on @Mamaduka comment; the following changes resolve it:
Use plugin_dir_path() to get the filesystem directory path:
$certfile = plugin_dir_path(__FILE__) . '/clientcert.pem';
$keyfile = plugin_dir_path(__FILE__) . '/clientkey.key';
Then remove getcwd().
If you want to use it in your theme use TEMPLATEPATH
I also want to mention that using the following paths previously did not work:
WP_PLUGIN_URL . "https://wordpress.stackexchange.com/" . plugin_basename( dirname(__FILE__) ) . '/clientkey.key'
nor:
get_bloginfo('template_directory') . '/lib/cert/clientcert.pem'
nor:
'http://my-web-site.com/clientcert.pem'