Custom Field – Do Not Show if Value is Empty?

Add a little check to your code

    function custom_do_grid_loop() {
    // Intro Text (from page content)
    echo '<div class="page hentry entry">';
    echo '<h1 class="entry-title">'. get_the_title() .'</h1>';
    if ( has_post_thumbnail() ) {
        echo '<div class="import-image">' . get_the_post_thumbnail() . '</div>';
    } 
    echo '<div class="entry-content"><p>' . get_the_content() . '</p>';
    //Add this condition to your code
    $meta = genesis_get_custom_field( 'article_reference' );
    //Remove white space from both sides,
    if( !empty(trim($meta)) ){
        echo '<div class="field_name"><strong>Article Reference:</strong> ' . genesis_get_custom_field( 'article_reference' ) .'</div>';
    }
    echo '</div><!-- end .entry-content -->';
    echo '</div><!-- end .page .hentry .entry -->';
    }

If its not empty show it, otherwise don’t.

Edited:

You can do something like this for further conditions

    if($meta == 20)
    {
        echo 'do 20';
    }
    elseif ($meta == 21)
    {
        echo 'do 21';
    }
    else
    {
        echo 'If all condition fails this will be echo';
    }