axis1 or axis2?
anyway.. if it's just https, you need to import the certificate and depending on the policy of the server you are calling you might have to present yourself with a certificate too.....
look here https://axis.apache.org/axis2/java/rampart/samples.html for information and an example on basic auth..
As for adding a certificate to the outgoing request you need to do something along these lines:
System.setProperty("javax.net.ssl.trustStoreType", "JKS");
System.setProperty("javax.net.ssl.trustStore", "keystore.jks");
System.setProperty("javax.net.ssl.trustStorePassword", "password");
System.setProperty("javax.net.ssl.keyStoreType", "pkcs12");
System.setProperty("javax.net.ssl.keyStore", "client.p12");
System.setProperty("javax.net.ssl.keyStorePassword", "password");
Take additional care if your communication is going through a proxy..