The restman service can accept 2 types of authentication either SSL client mutual or HTTP Basic. The error you have present is due to SSL client mutual being used by the certificate is not being presented by the client. You will need to ensure that the signer certificate for the client certificate is in the Manage Certificates list with the Trust Anchor and Signed Client Certificate option checked.
Note: If you are not including an Authorization header, then the response will be "Authentication Required".
Sincerely,
Stephen Hughes
Director, CA Support