How this process works:

Most insurance companies include an appraisal and/or arbitration clause, stating that the parties can demand an independent appraisal. If the value remains an issue, a third-party umpire can handle any disputes between the parties.

The arbitration process is similar but involves a panel vs. an individual umpire.

The Appraisal Clause may include the following language and is a good general explanation of how appraisal works:

If you and we fail to agree on the actual cash value or, if applicable, the replacement cost of your damaged property to settle upon the amount of loss, then either may demand an appraisal of the loss. In this event, you and we will each choose a competent and impartial appraiser within 20 days after receiving a written request from the other. The two appraisers will choose an umpire. If they cannot agree upon an umpire within 15 days, you or we may request that the choice be made by a judge of a court of record in the State where the covered property is located.

The appraisers will separately state the actual cash value, the replacement cost, and the amount of loss to each item. If the appraisers submit a written report of an agreement to us, the amount agreed upon will be the amount of loss. If they fail to agree, they will submit their differences to the umpire. A decision agreed to by any two will set the amount of actual cash value and loss, or if it applies, the replacement cost and loss.

Each party will pay its own appraiser and bear the other expenses of the appraisal and umpire equally.