Climate-induced extreme weather events, as well as other natural and human-caused disasters, have the potential to increase the duration and frequency of large power outages. Resilience, in the form of supplying a small amount of power to homes and communities, can mitigate outage consequences by sustaining critical electricity-dependent services. Public decisions about investing in resilience depend, in part, on how much residential customers value those critical services. Here we develop a method to estimate residential willingness-to-pay for back-up electricity services in the event of a large 10-day blackout during very cold winter weather, and then survey a sample of 483 residential customers across northeast USA using that method. Respondents were willing to pay US$1.7–2.3 kWh–1 to sustain private demands and US$19–29 day–1 to support their communities. Previous experience with long-duration outages and the framing of the cause of the outage (natural or human-caused) did not affect willingness-to-pay.