The plugin “Ambrosite Next/Previous Post Link Plus”
https://wordpress.org/plugins/ambrosite-nextprevious-post-link-plus/
..seems to do the job well
To further style the results, one could even use it like this
$prev = previous_post_link_plus( array('return' => 'id') );
query_posts('p='.$prev); while (have_posts()) : the_post();
[...your stuff here...]
endwhile; wp_reset_query();
$next = next_post_link_plus( array('return' => 'id') );
query_posts('p='.$next); while (have_posts()) : the_post();
[...your stuff here...]
endwhile; wp_reset_query();