I’ve come into this problem a few times while building out sites so I’ve built a quick function to automatically calculate and resize (height) videos on your blog/website.  This is especially helpful on a site chalk full of videos like craiggoodwill.com.  Without further ado:

function resize_video() {
	// this function is helpful when using a dynamit width on your iFrames for YouTube or Vimeo videos to automatically adjust the height
	$('.video iframe, .video object, .video embed').each(function(){
		var width = $(this).width();
		var vidheight = (width * 0.5625);
		$(this).css({height : vidheight});
	});
}

Then call your function on both load and resize.

$(window).load(function(){
	/* do the resize on load */
	resize_video();
});

$(window).resize(function() {
	/* do the resize on orientation change as well */
	resize_video();
});