General synonyms:
* Justification
* Exoneration
* Clearance
* Rehabilitation
* Absolution
* Acquittal
* Redemption
* Justification
* Validation
* Confirmation
* Verification
More specific synonyms:
* Reparation (when the act of vindication involves making amends for a wrong)
* Triumph (when the vindication is a result of a victory or success)
* Restoration (when the vindication involves returning something to its former state)
* Reaffirmation (when the vindication strengthens a belief or idea)
* Exaltation (when the vindication raises someone or something to a higher level of esteem)
The best synonym to use will depend on the specific context and the meaning you want to convey.