In Australian English, we spell 'honour' with a 'u', and take the same approach for 'honourable' and and 'honourably'. However, when it comes to the word 'honorary', the 'u' disappears.
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It's yet another of those annoying glitches in spelling you have no choice but to learn by rote. We also use the u-free spelling for 'honorarium' and 'honorific', but I suspect 'honorary' is the word you'll encounter most often.
This is one case where US English spelling is more consistent: since Americans spell 'honour' without a 'u' as 'honor' in all circumstances, there's no exception to learn here. However, that doesn't mean you can apply the principle in reverse and start using 'honourary' in Australia. Indeed, it seems more likely that in the future, we'll see the US spelling become more common in other contexts — but for plain old 'honour' as a noun, we haven't crossed that barrier yet, so you need to know when to use a 'u' and when to leave it out.
Ultimately, English spelling is not consistent in any version, and everyone simply has to learn the exceptions. Accuracy matters.
Lifehacker's Mind Your Language column offers bossy advice on improving your writing.