do_shortcode with custom field

Nice one, you were practically there – the key is to assign the $ecpt_imdb variable with the data returned from get_post_meta:

<?php if ( $ecpt_imdb = get_post_meta( get_the_ID(), 'ecpt_imdb', true ) ) : ?>

    <h3>About the Movie</h3>
    <?php echo do_shortcode( '[imdb]http://www.imdb.com/title/' . $ecpt_imdb . '/[/imdb]' ) ?>

<?php endif ?>

You’ll see I’ve also used the template tag get_the_ID(), which is the “correct” way of getting the current post ID.