You will need to call the selectmenu widget "refresh" method off of your <select> element
Assuming your have something like this...
<div data-role="fieldcontain">
<label for="select-choice" class="select">Choose shipping method:</label>
<select name="select-choice" id="select-choice">
<option value="1">One</option>
<option value="2">Two</option>
<option value="3">Three</option>
<option value="4">Four</option>
</select>
</div>
Then you can have some JavaScript like the following...
var listItems = [{ value: "standard", text: "Standard: 7 day" },
{ value: "rush", text: "Rush: 3 days" },
{ value: "express", text: "Express: next day" },
{ value: "overnight", text: "Overnight" }], options = "";
$.each( listItems, function(index, item) {
options += "<option value='" + item.value + "'>" + item.text + "</option>";
});
$( "#select-choice" ).empty().append( options ).selectmenu( "refresh", true );