How can I add a search feature to my Drupal 7 Zen child theme frontpage?
Your probably getting the warning because the function takes its argument by reference and to pass a variable by reference it needs to be defined. You're passing a function call which isn't a variable.

Try the following...

$search_form = drupal_get_form('search_form');
$search_box = drupal_render($search_form);
$variables['search_box'] = $search_box;