Saving Homeowners from Onerous Rate Escalations Act of 2013 or SHORE Act of 2013 - Amends the National Flood Insurance Act of 1968 to direct the Administrator of the Federal Emergency Management Agency (FEMA) to phase in, over an eight-year period, any increase in the flood insurance risk premium rate caused by the prohibition against extending subsidies to new or lapsed policies.
Extends from a 5-year to a 10-year period the phase-in period for premium adjustment increases in the flood insurance risk rate. Prescribes a phase-in rate of: (1) 5% for each of the first 5 years after the effective date of an update, and 15% for each of the 5 ensuing years; and (2) 5% for each of the first 5 years following the effective date of designation as a special flood area of any area not previously so designated, and 15% for each of the 5 ensuing years.