Below is how I achieved a responsive jQuery UI Dialog.
To do this, I added a new option to the config - fluid: true, which says to make the dialog responsive. 
I then catch the resize and dialog open events, to change the max-width of the dialog on the fly, and reposition the dialog.
You can see it in action here: http://codepen.io/jasonday/pen/amlqz
Please review and post any edits or improvements.
// Demo: http://codepen.io/jasonday/pen/amlqz
// movemaine@gmail.com
$("#content").dialog({
    width: 'auto', // overcomes width:'auto' and maxWidth bug
    maxWidth: 600,
    height: 'auto',
    modal: true,
    fluid: true, //new option
    resizable: false
});
// on window resize run function
$(window).resize(function () {
    fluidDialog();
});
// catch dialog if opened within a viewport smaller than the dialog width
$(document).on("dialogopen", ".ui-dialog", function (event, ui) {
    fluidDialog();
});
function fluidDialog() {
    var $visible = $(".ui-dialog:visible");
    // each open dialog
    $visible.each(function () {
        var $this = $(this);
        var dialog = $this.find(".ui-dialog-content").data("ui-dialog");
        // if fluid option == true
        if (dialog.options.fluid) {
            var wWidth = $(window).width();
            // check window width against dialog width
            if (wWidth < (parseInt(dialog.options.maxWidth) + 50))  {
                // keep dialog from filling entire screen
                $this.css("max-width", "90%");
            } else {
                // fix maxWidth bug
                $this.css("max-width", dialog.options.maxWidth + "px");
            }
            //reposition dialog
            dialog.option("position", dialog.options.position);
        }
    });
}
EDIT
Updated approach:
https://github.com/jasonday/jQuery-UI-Dialog-extended
The repository above also includes options for:
- Click outside of dialog to close
- Hide title bar
- hide close button
- responsive (to address above)
- scale width & height for responsive (ex: 80% of window width)