Fire Damaged Home Rebuilding Act of 2013 - Amends the National Flood Insurance Act of 1968 to allow local variances for certain residential structures.
Prohibits certain land use and control measures from being deemed inadequate or inconsistent with land management criteria for participation in the flood insurance program because such measures authorize granting a variance for a residential structure located in a covered area and that is substantially damaged by fire.
Prohibits the Administrator of the Federal Emergency Management Agency (FEMA) from either suspending a community from participation in the national flood insurance program, or placing it on probation, because its land use and control measures provide for such a variance.
Defines such variance as one granted by an appropriate official of the community from compliance with such land use and control measures and permits repair and restoration of such structure to its pre-damaged condition without elevation of the structure.
Requires the official to have made specified determinations as a prerequisite to granting such a variance.
Requires chargeable flood insurance premium rates for a residential structure granted such a variance to equal, after repair and restoration, the rates which would have been applicable if the structure had not been substantially damaged, repaired, and restored under the variance.