The following works:
openssl s_client -key private_key.key -cert cert.crt -connect "client-auth.myhost.com:443"
wget --no-check-certificate --certificate=cert.crt --private-key=private_key.key https://client-auth.myhost.com:443/path
Yet curl does not seem to work:
curl -v -s -k --key private_key.key --cert cert.crt "https://client-auth.myhost.com:443/path"