exculpate
To prove someone is not guilty or not to blame.
To exculpate someone means to clear them of blame or prove they're not guilty of something they were accused of doing wrong. When new evidence exculpates a suspect in a mystery, it shows they couldn't have committed the crime. If your teacher initially thinks you copied homework but then discovers you worked on it before the other student did, that timeline exculpates you.
It's stronger than simply making an excuse: exculpating evidence actually proves innocence. In court, a lawyer might present fingerprints or security camera footage that exculpates their client by showing someone else committed the crime.
You might see the related word exculpatory, which describes evidence or information that clears someone of guilt. If witnesses come forward with exculpatory testimony, they're providing information that proves someone's innocence. The opposite would be inculpatory evidence, which suggests guilt.
The word carries a formal, serious tone because it usually involves significant accusations. You wouldn't say your friend exculpated you for taking the last cookie, but you might say a video recording exculpated someone wrongly accused of vandalism.