exculpation

[Cf. LL. exculpatio.]
The act of exculpating from alleged fault or crime; that which exculpates; excuse.

These robbers, however, were men who might have made out a strong case in exculpation of themselves.

noun

A freeing or clearing from accusation or guilt: exoneration, vindication. Law acquittal. See law.

The noun has 2 meanings:

Meaning #1: a defense of some offensive behavior or some failure to keep a promise etc.
  Synonyms: excuse, alibi, self-justification

Meaning #2: the act of freeing from guilt or blame