Since there's no signal anyway, I set my phone to "airplane mode," which powers off the cellular, Wi-Fi, and Bluetooth radios. Not only does this bypass the frequent and annoying pop-up messages warning me that there's no signal, but with all the radios off, the battery lasted far longer. GPS, of course, is unaffected because it receives only -- it doesn't transmit.
I recounted this story to my editor when I returned, and she replied, "Even when you're on vacation, there's no escape from Business Hacks research." She's right, and there you go.