You’re probably familiar with UPS battery backups that are designed to keep a PC running in the event of a power interruption, but this model from APC is designed specifically for mobile devices and networking gear.
For $60, it’ll keep your modem and router powered on for up to two hours, and the battery portion is actually removable, and can be used as a USB battery pack for your phone. That price is the best Amazon’s ever offered, but it’s only available for Prime members.