If you do not want to use logon tickets in your system landscape, you need to manually configure the trust relationship between the systems and exchange the certificates.
Export the WS provider certificate.
More information: Exporting the AS ABAP Certificate
Import the WS provider's certificate into the WS consumer.
More information: Trust Manager
Export the WS consumer's certificate.
More information: Exporting the AS ABAP Certificate
Import the WS consumer certificate into the WS provider.
More information: Trust Manager
Include the imported certificates in the access control lists of systems, if necessary