Both medicare and UnitedHealthcare have an appeals process if a medical claim is denied.
The Medicare appeals process is dictated by the government and there are 3 levels of appeal. At the first level you are basically still dealing with administrative personnel. At the second level you are finally reaching medical professionals. When you appeal a claim you will need supporting information from your doctor as to why the procedure was necessary which can make it a little bit of a hassle to appeal. Some doctors have staff that help with appeals. It is a cost overhead headache and no wonder medical professionals are opting out of treating medicare clients given the fee structure is pathetically low. Even if your doctor is not much help - still gather your evidence and appeal! For example, Medicare routinely denies screening tests (e.g, EKG or blood tests). If you had those tests as a prep for surgery then submit copies of the bills showing the surgery. Of course, the logical assumption is Medicare would have realized you had surgery since they pay that claim as well. Don't get logical. Do appeal.
For UnitedHealthcare there is also an appeal process. However, because the IBM supplemental plan is not a government sanctioned medigap plan the appeal process is strickly a UHC process. It is perhaps a reason why you might want to consider buying a legit medigap plan. If you have a medigap plan then your appeal is going through government agencies at the second and third level. For IBM's supplemental plan if UHC denies the appeal your recourse it to complain to your state health insurance agency. It is a harder process and the chances of UHC being overturned are likely lower but those complaints are "registered" against UHC to help the state agency to look for patterns. So, use the UHC appeal process and the state complaint process. It may also be worthwhile to lodge a complaint with IBM if you think UHC is being unreasonable.
There is also an appeal process for drug plans. If the IBM plan (Medco) is denying coverage for a drug use the appeal process if the drug is not on Medicares "never cover" list. Don't waste your time appealing drugs on the "never cover" list. Most of them fall into the category of barbituates. You can get a list of those drugs from Medicare. Often times, coverage is also denied if the drug is being used "off label". That appeal argument is easier to win.