Testing RestAPI with WebHTTP - problem with SSL



I am trying to run a very simple test using the WebHTTP protocol to send an XML message to an API.  The test itself is working correctly when run against a URL that is not using SSL.  However, when running against the URL which *is* using SSL, I am getting the following error message:


Error -27774: Server "[my server name]" shut connection during attempt to negotiate SSL session


This test was created manually, without recording anything.  I have tried getting the PEM certificate and including it in the test, in both the "Recording Settings" dialog, as well as using web_set_certificate_ex function in the test. 


Here is my code:


    lr_start_transaction("001 Do Something");
    web_add_header("Accept", "application/xml");
    web_add_header("source-id", "234");
    web_add_header("Content-Type", "application/xml");
    web_custom_request("Custom Request",
    lr_end_transaction("001 Do Something",LR_AUTO);
    return 0;