i used this on my jekyll site, works like a charm. not sure how far back the browser support goes, but works on all modern ones.
this was largely figured out by Young Hahn and Garret Miller.
<div class='vid-frame' style='width: 100%; height: 0px; padding-bottom:56.25%; position:relative;'>
<iframe mozallowfullscreen='mozallowfullscreen' src='http://player.vimeo.com/video/YOUR-VIDEO-NUMBER-HERE' webkitAllowFullScreen='webkitAllowFullScreen' allowFullScreen='allowFullScreen' frameborder='0' height='100%' width='100%' style='position:absolute'> </iframe>
</div>