ElectronでBrowserWindowやwebviewの証明書エラーに対処する ref: http://qiita.com/yuya-oc/items/2764bf7a33c751498858

file0.js

app.on('certificate-error', function(event, webContents, url, error, certificate, callback) {
  event.preventDefault();
  callback(true);
});

file1.js

app.on('certificate-error', function(event, webContents, url, error, certificate, callback) {
  event.preventDefault();
  electron.dialog.showMessageBox(mainWindow, {
    title: 'Certificate error',
    message: `Do you trust certificate from "${certificate.issuerName}"?`,
    detail: `URL: ${url}\nError: ${error}`,
    type: 'warning',
    buttons: [
      'Yes',
      'No'
    ],
    cancelId: 1
  }, function(response) {
    if (response === 0) {
      callback(true);
    }
    else {
      callback(false);
    }
  });
});