You can use .html() if you wrap the jQuery object with a parent element first and then call .html() on the parent element.
var $xml = $(somexmlstring);
$xml.find('name:contains("' + somevalue + '")').remove();
var newxmlstring = $('<x></x>').append($xml).html();
This works even if the original XML string does not have a single root element. It does not work, however, if the original XML string contains an XML declaration (like <?xml version="1.0" encoding="UTF-8"?>).
jsfiddle
If the original XML string is a valid XML document, optionally containing an XML declaration at the beginning, you may want to create the jQuery object like this:
var $xml = $($.parseXML(somexmlstring).documentElement);
$xml.find('name:contains("' + somevalue + '")').remove();
var newxmlstring = $('<x></x>').append($xml).html();
jsfiddle