It depends on how the user has things set up as to what requires a passcode, but almost* anything that requires the user to unlock their device will result in an Emergency button being present on the screen. Generally swiping to the Today/widget screen and tapping on something that causes an app to try and open would result in a passcode screen.
You're correct in that it's not quite as intuitive as it was prior to iOS 10.
* I did notice if you swipe right, to the Today/widget screen, tapping the Edit button at the bottom results in a passcode entry screen that does not have an Emergency button.