Insert the current theme header into an external HTML/XHTML file

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The key to answer was found on SO; here is the solution for my case:

create a PHP file with the following:

<?php
define('WP_USE_THEMES', false);
require('path/to/your-wordpress-dir/wp-blog-header.php');
get_header();
?>
//Contents of the body of your XHTML page go here
<?php get_footer(); ?>

Now you have an external page in the format of your WordPress theme.