For one-off, you can use a bookmarklet:

For example, Wayback Machine:

Save Current URL: javascript:q=(document.location.href);void(open('http://web.archive.org/save/*/'+location.href.replace(/https..., ""),'_self ','resizable,location,menubar,toolbar,scrollbars,status'));

GoBack Current URL: javascript:q=(document.location.href);void(open('http://web.archive.org/web/*/'+location.href.replace(/https?..., ""),'_self ','resizable,location,menubar,toolbar,scrollbars,status'));