It matters which UM you are speaking about and which state your coverage is in, but typically UM covers in the case of a hit and run.

UMBI (Bodily Injury) covers you, the insured members of your household and your passengers for bodily/personal injuries, damages or death caused by an at-fault uninsured or hit-and-run driver. If you are involved in an accident where the other driver is at fault but has no insurance, your policy will cover your medical expenses, up to the limit on your policy.

UMPD (Property Damage) covers your auto when property damage is sustained by an insured and the negligent operator does not possess insurance.

After reporting the claim, your claims adjuster will be able to determine if there are any mitigating factors that would not allow coverage in your situation.