How to pass context down to the Enzyme mount method to test component which includes Material UI component?

Try adding childContextTypes in the mount options:

return mount(
  <SearchBar {...props} />, {
    context: {muiTheme},
    childContextTypes: {muiTheme: React.PropTypes.object}
  }
);

By doing it you set the Enzyme wrapper to make the muiTheme available to it’s children through the context.