They can't be 100% certain. They use a statistical argument, but the odds that it can happen are about the same as one monkey typing the whole of Shakespeare on his first attempt while simultaneously building a space shuttle from things he found in a skip.

From comparing the mass of a proton (1.7 * 10^-27) to the mass of a snowflake (3 milligrams - very rough averages will do) there seem to be about 10^18 water molecules in a snowflake. Snow crystals seem to grow randomly from individual water vapour molecules, and then about 100 crystals agglomerate into a snowflake. So the number of potential distinct snow crystals is the number of permutations of 10^16 objects, any number at a time. This is beyond astronomical - I think it might have around 10^13 digits.

Covering the whole earth 1 kilometre deep in ice seems to be about 5 * 10^17 tonnes, or about 2 * 10^26 snowflakes, i.e. only a 27 digit number. So the number of pairs of snowflakes that might be identical is only a 54-digit number. compared to a ten-trillion-digit number of possible variations.

On those odds, you could search your whole lifetime and not even find two snowflakes with the same number of water molecules, let alone the same arrangement of them.

However, the scale on which you declare two snowflakes "identical" matters. At any normal freezing temperature, molecules wander around all the time by solid-to-gas phase changes. Just freezing them harder will affect the structure anyway. If you can only see them with visual-light microscope, an awful lot of molecule-level differences will not be detectable. So at some limit of practical comparison, there will be identical snowflakes. That's a matter of classification, not molecular identity.

Anyway, what would your criterion for identity be? Suppose that miraculously you did get two of Pedant's snowflakes with exactly the same number of water molecules and the same impurities, and you did, even more miraculously find them with the molecules in exactly the same configuration. (Now, note well; by this time we are talking of numbers of alternatives so great that we could expect to find no duplicate, not just on one planet, but in the entire observable universe! But never mind that; just accept the miracle for now.)

Within a microsecond (Why a microsecond? Well, why not a microsecond? choose your own time unit.) millions of molecules ould have evaporated from each flake, millions more would have condensed. By now they are no longer identical. In which microsecond did you observe them to be identical, and how did you establish their identity?

Note also that in spite of their breathtaking complexity and beauty, the precision of snowflakes is not absolute.  Examine photographs of snow crystals carefully. You will find slight imperfections that differ from branch to branch of the same flake. Does that suggest a slight difficulty?

And finally, Even if you do decide to ignore the nonsense of worrying about minor imperfections and accept that if two snowflakes look about the same and are about the same size, then they are close enough for government work.  You will find that there are plenty of discrepancies for the government inspector to quibble about. Even if you did find two the same for all practical purposes, you would have a hard time persuading even a reasonable sceptic, let alone a real nit-picker. 

But think about your moment of fame: "Look Mabel! Look! There he goes! I bet that is the guy we saw on TV! Remember? The one who found two beer cans with the same serial number! Or was it banknotes...? Snowflakes? Don't be silly, girl! But never mind, do you suppose he gives autographs...?"

Naaahhh... Not reeeally...!

Let's worry about something more exciting; identical acorn cups or the like.

I'm worrying already,

Jon