Sins begin of 206 you can get free ssl certificates from letsencrypt. These certificates can also be used for Zimbra OSC mail server. By using this you no longer need the selfsigned certificates.
Installing letsencrypt on Ubunutu
Generating new certificates
Installing ssl certificate in Zimbra
Normaly Letsencrypt works “out-of-the-box” but with Zimbra you need to get the “DST ROOT CA X3” certificate. You can copy and past this in the file
Deployment of ssl in Zimbra
After this your certificate is installed in Zimbra. Only be aware that these certificates are only 3 months valid.