With the CURLOPT_REFERRER option, which you had already made use of.
curl_setopt($ch, CURLOPT_REFERER, "your referer website");
[EDIT]
I don't think that website can find referer of your localhost website.
Try this on Google Chrome Browser
In the Developer Tools, go to the Network view (if it wasn't open when you loaded the page, you'll need to reload to get it populated).
Click on the main page request -- it should be at the top of the list.
When you click, the right pane will probably show the HTML for it.
Click on the "Headers" tab on the right side.
The Referer is shown in the list of Request Headers.
