This is a modified extract from Bill Erickson's Genesis 404 Page plugin (https://github.com/billerickson/Genesis-404-Page). This bit of code adds shortcode support for a search form within a Genesis page or post.

search_shortcode.php

<?php

add_action( 'init', 'cd_register_shortcode' );
/**
* Register shortcode with the theme
*/
function cd_register_shortcode() {
  add_shortcode( '404-search', 'cd_search_shortcode' );
}

/**
* Search Shortcode Excerpt
*/
function cd_search_shortcode() {
  return '<div class="404-search">' . get_search_form( false ) . '</div>';
}