Is compensation due if someone accuses me of damaging something, and I am not sure if I did?

The fundamental principle is the presumption of innocence (bā'at adh-dhimmah), and certainty is not removed by doubt. Therefore, compensation is not obligatory unless the one who caused damage is certain or strongly believes that he damaged something. This applies to the matter between him and Allah. However, before a court of law, compensation is not obligatory unless the claimant provides evidence.