If you are writing your own results template, or modifying one from your theme, you can use PHP to test for the number of results and use an IF statement to conditionally load the content loop or the special message. When you use our Shortcode Results display method, that uses our own template, which you can find in the plugin’s template folder. In that, you can see how we do as I have described, when using the standard WP Query for the loop.

See if this fixes the nor results message:

<?php
$custom_terms = get_terms('alfabet');
if (!empty($custom_terms)) {
  foreach($custom_terms as $custom_term) {
  wp_reset_query();
    $args = array(
      'post_type' => 'bontvrijlijst',
      'search_filter_id' => 7242,
      'posts_per_page' => -1,
      'orderby'=> 'title',
      'order' => 'ASC',
      'tax_query' => array(
        array(
          'taxonomy' => 'alfabet',
          'field' => 'slug',
          'terms' => $custom_term->slug,
        ),
      ),
    );

    $loop = new WP_Query($args);
    if($loop->have_posts()) {
      echo '<div id="' . $custom_term->slug . '" class="alfabet-letter-wrap"><div class="alfabet-letter">'.$custom_term->name.'</div><ul class="members">';
      while($loop->have_posts()) : $loop->the_post();
        $company_link = get_field('url');
        echo '<li class="member"><a href="'. $company_link .'" target="_blank">'.get_the_title().'</a></li>';
      endwhile;
      echo '</ul></div>';
    } else {
  echo '<p><strong>Er zijn geen bedrijven die voldoen aan deze zoekopdracht. Probeer het opnieuw.</strong></p>';
    }
  }
}
?>

I think the else was in the wrong place.

Ah, I see why. You are looping through custom terms one after the other, and only doing the actual wp_query inside each loop. That way you can have only one no results for each custom terms (the alphabet letters) or none at all. So, instead you have a test variable and set this to 0. Every time you find results in each loop, you increment that variable. If it is still 0 at the end, then no results were found:

<?php
$custom_terms = get_terms('alfabet');
$empty_test = 0;
if (!empty($custom_terms)) {
  foreach($custom_terms as $custom_term) {
  wp_reset_query();
    $args = array(
      'post_type' => 'bontvrijlijst',
      'search_filter_id' => 7242,
      'posts_per_page' => -1,
      'orderby'=> 'title',
      'order' => 'ASC',
      'tax_query' => array(
        array(
          'taxonomy' => 'alfabet',
          'field' => 'slug',
          'terms' => $custom_term->slug,
        ),
      ),
    );

    $loop = new WP_Query($args);
    if($loop->have_posts()) {
					$empty_test++;
      echo '<div id="' . $custom_term->slug . '" class="alfabet-letter-wrap"><div class="alfabet-letter">'.$custom_term->name.'</div><ul class="members">';
      while($loop->have_posts()) : $loop->the_post();
        $company_link = get_field('url');
        echo '<li class="member"><a href="'. $company_link .'" target="_blank">'.get_the_title().'</a></li>';
      endwhile;
      echo '</ul></div>';
				}
  }
}
if ($empty_test > 0) {
	  echo '<p><strong>Er zijn geen bedrijven die voldoen aan deze zoekopdracht. Probeer het opnieuw.</strong></p>';
}
?>

You might want to echo the $empty_test variable at each iteration to see what it is at?

Face -> Palm

That was my bad in the coding. One = sets the parameter, Two tests it. D’oh. Are we done here?