Poised on a surfboard and dwarfed by a tower of water some 10 times her size, fear is one of the first emotions that big wave surfer Laura Crane feels before she hurtles down a 60-foot behemoth.

The threat of those waves is not baseless: big-wave waterman Mark Foo drowned at California’s Mavericks in 1994, while Hawaii local Todd Chesser died surfing a huge swell on an outer reef off ...