I reported this at Search Engine Land on Friday and to be honest, it is not a feature most of you will benefit from, but if you want, you can force Google's SSL off and search insecurely and thus pass your query data to webmasters by using google.com/webhp?nord=1 instead of google.com.
The benefits are limited in that you need to specifically do this yourself. Of course, you can build a browser extension to automate this but since 99.999% of people won't do this, it won't help you get search query data. But it is good to know you can do this, if you do want to disable SSL on Google.
So either go to google.com/webhp?nord=1 or add "?nord=1" to a Google search URL after "www.google.com/", while replacing "https" with "http".
Forum discussion at Google Web Search Help.