If the image variable is specified, show image, if not no code

you just have to check if it exists before outputting any markup.

<?php
$postimage = get_post_meta($post->ID, 'postimage', true);
if($postimage):
?>
    <img src="https://wordpress.stackexchange.com/questions/26809/<?php echo $postimage; ?>" />
<?php
endif;
?>