If you have compiled the netcdf4 and hdf5 libraries statically (in my case, because I want to deploy to AWS Lambda), then the module is built but it cannot be loaded due to missing symbols:

Error: node_modules/netcdf4/build/Release/netcdf4.node: undefined symbol: H5T_NATIVE_SHORT_g
    at Object.Module._extensions..node (internal/modules/cjs/loader.js:718:18)
    at Module.load (internal/modules/cjs/loader.js:599:32)

It turns out this is due to a missing library dependency in binding.gyp, and the solution is to specify the dependent library:

{
  "targets": [
    {
      "libraries": [
        "-lnetcdf",
        "-lhdf5"       # Must specify
      ],
...

I haven't been able to test this with shared libraries (as my environment is only building static ones) but if it doesn't break the shared library build, could this change be included for the benefit of those using static libraries?