To pay compensation for a loss, damages, or similar expense is to indemnify. "The insurance company indemnified its customers for their claims after the severe storm — one customer lost three cars, a row boat, and a golf cart."
The verb indemnify also means to secure against future loss. The farmers bought insurance to indemnify themselves and their animals against catastrophic loss. The word indemnify comes from the Latin word indemnis, which means "to unhurt." The city wanted to shut down an old local landmark because they were afraid it no longer met modern safety standards, but local citizens wanted it to remain. In a compromise, the owners agreed to indemnify the city against possible loss and the landmark was allowed to remain.