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Self-Signed Certificate on your Zimbra server is expired? Follow the instructions given below, and you will be back online asap.

1. Begin by generating a new Certificate Authority (CA).

/opt/zimbra/bin/zmcertmgr createca -new

2. Then generate a certificate signed by the CA that expires in 365 days.

/opt/zimbra/bin/zmcertmgr createcrt -new -days 365

3. Next deploy the certificate.

/opt/zimbra/bin/zmcertmgr deploycrt self

4. Next deploy the CA.

/opt/zimbra/bin/zmcertmgr deployca

5. To finish, verify the certificate was deployed to all the services.

/opt/zimbra/bin/zmcertmgr viewdeployedcrt

Resetart your zimbra and you will be good.
I have this tested against Zimbra 8.

Reference: https://wiki.zimbra.com/wiki/Administration_Console_and_CLI_Certificate_Tools#ZCS_6.0.x_and_5.0.x