The wp_nav_menu()
function has an items_wrap
parameter which contains this by default:
<ul id="%1$s" class="%2$s">%3$s</ul>
So you can pass it the above default plus any appended string:
$search_form = get_search_form( false ); // Return not echo
$items_wrap = '<ul id="%1$s" class="%2$s">%3$s';
$items_wrap .= sprintf( '<li id="searchItem">%1$s</li></ul>', $search_form );
wp_nav_menu( array(
'items_wrap' => $items_wrap,
) );