I do this jobs many times with good result.
I make this.
1- install the new server, if possible the same OS that the old one.
2- Install dependences to make possible to install zimbra from scartch. ( in my case debian dependences, a nice howto in howtoforge)
3. download the same zimbra version as the old server
4. run installer int he new server ./install.sh -s "( -s is important)"
5. remove the /opt/zimbra from the new server "rm -rf /opt/zimbra"
6.Install rsyn in both servers and rsync the old server with the new one, in the old server run "rsync -e ssh -avz /opt/zimbra root@ip_new_server:"
7. take a wile, take a break a sit with a coffe..
8. when finish.. then in the new server you have a zimbra directory under root, move it to /opt/ "mv /root/zimbra /opt/", run in the new server again ./install.sh (without -s)
9. when installer ask for upgrade, say "yes"
regards.
B.