I had a game against dwarfs yesterday [which I lost], and I'm having trouble against them.
The dwarfs themselves I can kill with ease, but both my sphinxes died within 2 turns thanks to his cannons, but the real problem is the anti-magick.

He had 3 dispel runes, another dispel rune that could make my wizard forget the spell on a 4+, and a 5th one that instantly ended the magick phase, not to mention the extra 3 dispel dice he was getting each turn, as well as an item that stole one of my power dice and added it to his dispel pool each turn.

So my question is, is there anything I can do against this? I didn't get a single spell off all game, even though I had the casket and Arkhan giving me 11 power dice in each phase.

First off, that sounds illegal. There is no item that the dwarves have access to that ends the magic phase. Period. If they did, it would be used all the time, but it doesn't exist (unless it was a special character, but I don't think those have it either). So either your opponent was confused or cheating but either way, their anti-magic capability isn't quite that good.

But aside from that, in general yes, the dwarves will shut down your magic phase. Pretty much entirely, pretty much all the time. The trick to that is that in early turns you need to cast a few big spells to try and draw out any dispel scrolls he has. So cast bubble 5+ ward and he will either have to chuck a lot of dice at it or use a scroll. But this way hopefully by the later turns, he will have run out and you can have a little more freedom. The other trick is to just 6-dice the casket every turn and hope for IF. Then it will march down his artillery line and even if it doesn't kill anything outright, it will still probably be doing a few wounds and at least you are getting a spell through and forcing those tests.

Not much else to be done though. Normal magic tactics don't work against dwarves. Just be glad that he has invested all those points into anti-magic rather than more guns or GW-troops.

I WAS chucking 6 dice at the casket.
No luck, and it was dispelled every time.

That'll happen. You have to go for maximum power casts (ie 6 dice caskets) and hope for ultimate force. Or go all out with maximum number of casts (ie several 2-dice casts with a lvl 4 & heirotitan) - and force him to burn his dispel dice so you can get one spell through at the end of the round.

Neither is garaunteed to work- but treating it like a normal magic phase is pretty much garaunteed not to work. You have to go to one extreme or the other with stunties.