responsive-iframes.css

iframe {
  max-width: 100%;
}

responsive-iframes.html

<!-- All you need is a defined width & height -->
<iframe frameborder="0" height="900" width="1600" src="http://example.com/"></iframe>

responsive-iframes.js

var iframe = {
    adjustIframes: function() {
        iframe.$iframe.each(function() {
            var $this       = $(this),
                proportion  = $this.data( 'proportion' ),
                w           = $this.attr('width'),
                actual_w    = $this.width();

            if ( ! proportion ) {
                proportion = $this.attr('height') / w;
                $this.data( 'proportion', proportion );
            }

            if ( actual_w != w ) {
                $this.css( 'height', Math.round( actual_w * proportion ) + 'px' );
            }
        });
    },
    init: function() {
        this.$iframe = $('iframe');
        if (this.$iframe.length) {
            this.adjustIframes();
            $(window).on('resize load', iframe.adjustIframes);
        }
    }
};