A month ago (almost exactly), Google announced their new Hum feature-- there's a great marketing video they made, if you want to watch that.
Using the latest version of the Google app, Google now lets you search for a song by humming for 10-15 seconds. You can use this on your iOS or Android devices by clicking on the microphone and selecting the "Search a song" button.
I can assure you, this most definitely worked for me. You don't even have to be a good singer (which is true for most of us, surely).
Google uses machine learning to identify potential song matches, and gives a % rating for the likelihood of each song being the one you hummed; i.e. after humming for 10-15 seconds, Google presents a short list (3) of potential songs it could be, and rates each ones potential match.