In the appraisal process you hope that both appraisers can fairly and competently come to agreement. Sometimes they can't and that is when you need someone who is qualified to decide who is correct in assessing your claim. According to the Windstorm Insurance Network, an umpire is a competent, disinterested, impartial individual who is charged with making a decision regarding the value of property or the amount of a property loss. In the property insurance world an umpire is an appointed professional in an insurance claim dispute who makes a binding decision after the two parties in an appraisal process fail to agree on a loss. In short, an umpire is a trained dispute resolution expert who should also have some experience in understanding insurance adjusting and all its components. The option to appoint an umpire is typically part of an appraisal process found in most property policies, although a few insurance companies have actually removed this to our surprise. This is a process that can help both sides avoid the cost of litigation while reaching a mutually beneficial resolution. 
Most insurance policies include an Appraisal Clause or Appraisal Provision which provides an option to the policyholder to dispute an insurance claim when the insured and the insurer cannot agree on the amount to repair the loss. The basis of the process is quite simple and is explained below. Your policy may even include similar verbiage...

If you and we fail to agree on the amount of loss, either may demand that the amount of loss be set by Appraisal.  If either makes a written demand for Appraisal, each shall select a competent, independent appraiser.  Each shall notify the other of the appraiser’s identity within 20 days of receipt of the written demand.  The two appraisers shall then select a competent, impartial Umpire.  If the two appraisers are unable to agree upon an Umpire within 15 days, you or we can ask a judge of a court of record in the state where the residence premises is located to select an Umpire.  The Appraisers shall then set the amount of the loss.  If the Appraisers fail to agree within a reasonable time, they shall submit their differences to the Umpire.  Written agreement signed by any two of these three shall set the amount of the loss.

With certifications as an appraiser and umpire, and civil mediation, with extensive claims experience Insurance Adjusters Group can provide you with a competent and impartial umpire services.