Health insurance claims can be appealed by submitting the proper forms to your health insurer. If a claim is denied or paid incorrectly, in your estimation, every health insurer must allow you to appeal how the claim was paid. Your appeal may be denied but the health insurer must allow you to appeal the claim. An appeal is near the end of the process for claims being denied or paid incorrectly. There are some other steps in advance of a health insurance claims appeal that can be completed to attempt to get the health insurance claim processed.