The solution is to input Unicode characters (see here: http://www.unicode.org/charts/PDF/U1F300.pdf, 1f36c for example) with the keyboard of a Dell Latitude e6420 which, a quick Google image search tells us looks like:
. Notice in the picture how the orange keys Fn allows access to a "numeric keypad" type function.
Question then is: how can one input the Unicode character 1F36C using the keyboard only?