For the VertiGIS Integrator to access the map service in the ArcGIS Server via HTTPS, the SSL certificate used in the ArcGIS Server must first be imported into the Java Runtime Environment.

1.Run cmd in administrator mode and switch to the Java jre/bin directory, e.g:

2.Perform now the following command to import the certificate
 
keytool -importcert -file [path to certificate] -alias [arbitrary name for the entry in the certificate store] -cacerts
 

3.Enter changeit as default password for the Keystore
Afterwards, the certificate is issued. Answer the question Trust this certificate? with Yes.

4.Restart Tomcat

Now you can access a map service via HTTPS in the configuration settings (Settings > Parameter).

For more details check out the ArcGIS Server chapter.