Esse codigo tá mal...
Correcto:
<center><?php if(get_post_meta($post->ID, 'designed-by')){ ?><li class="designer"><a href="<?php echo get_post_meta($post->ID, 'designed-by', $single = true); ?>"><img src='http://xxxxxxxxx.com/wp-content/themes/MyXXX/images/autor.png' border='0'/></a></li><?php } ?>
<?php if(get_post_meta($post->ID, 'web-url')){ ?></center>
Faltava-te fechar a tag a.