Can't get SSL Authentication to work

Our SAP server is supposed to call an external web service, which requires authentication via an SSL certificate. So in STRUST I have created a new client certificate, which has been imported on the external server. Also we have received the servers' certificate, which has been added to this new entry in STRUST.

In SOAMANAGER I have set this new STRUST entry to be used for authentication at the web service provider.

Now when our SAP machine calls the remote web service, authentication fails.

In the ICM logs the following error messages are given:

[Thr 140543812142848] SecuSSL_SessionStart: SSL_connnect() failed  (536875072/0x20001040)

[Thr 140543812142848]    => "SSL API error"

[Thr 140543812142848] >>            Begin of Secu-SSL Errorstack            >>

[Thr 140543812142848] 0x20001040   SAPCRYPTOLIB   SSL_connect

[Thr 140543812142848] SSL API error

[Thr 140543812142848] received a fatal SSLv3 handshake failure alert message from the peer

[Thr 140543812142848] 0xa0600266   SSL   ssl3_read_bytes

[Thr 140543812142848] received a fatal SSLv3 handshake failure alert message from the peer

[Thr 140543812142848] <<            End of Secu-SSL Errorstack

[Thr 140543812142848]   SSL_get_state()==0x21d0 "SSLv3 read finished A"

[Thr 140543812142848]   No certificate request received from Server

[Thr 140543812142848]   SSL NI-hdl 401: local=10.156.32.11:62224  peer=10.206.58.12:16101

[Thr 140543812142848] <<- ERROR: SapSSLSessionStart(sssl_hdl=0x7fd2d0099410)==SSSLERR_SSL_CONNECT

Any ideas what we might be missing here?