How to retrieve a select box option and set the field's value to it?
This question looks a little old, but here is an answer for you.  Reading your comments you have 

//Declare the callback for after_build for page node form
function set_keywords_form_alter(&amp;$form, &amp;$form_state, $form_id) {
    if ($form_id == 'part_node_form') {
        $form['#after_build'][] = 'set_keywords_after_build';
    }
}

function set_keywords_after_build($form, &amp;$form_state) {
    $keyword = $form['field_product_keyword']['und']['#options']; 
    $form['field_product_keyword']['und']['#value'] = $keyword;
    $form['field_product_keyword']['und']['#default_value'] = $keyword; 
    return $form; 
}


I applaud your efforts, especially that you are attempting to do this clean and proper with a hook_after_build.  The hook_after_build allows your value setting code to run after the Reference Field Option Limit has done its adjustments, so you are certain to be getting the value you want.
I see one mistake in your code, and that is that #options is an array of Label => Value so that the form can display language in the select field instead of raw values.  I think all you need is this one adjustment:

// remove the -None- option from the start, then set the next option
array_shift($form['field_product_keyword']['und']['#options']);
$keyword = array_shift(array_keys($form['field_product_keyword']['und']['#options']));
// this is safe because $form is not passed by reference, 
// do not do this on $form_state


When trying to do things like this, I find it helpful to look inside what it is I am manipulating.  If you know the string of references that you need to access some data, you can print it on the form like this:

//Declare the callback for after_build for page node form
function set_keywords_form_alter(&amp;$form, &amp;$form_state, $form_id) {
    if ($form_id == 'part_node_form') {
        $form['#after_build'][] = 'set_keywords_after_build';

        // see what our options are, print them as text on the form:
        $form['some_text'] = array(
            '#markup' =&gt; '&lt;p&gt;'. $form['field_product_keyword']['und']['#options'][0] .'&lt;/p&gt;',
            '#weight' =&gt; '-80'
        );
    }
}


As you have mentioned you are using the devel module, you could easily throw the #options array into a dpm() or krumo() inside the form alter and get it printed to your form page also.