I do not want to advocate it is the best solution – I don’t even go as far as saying it is a solution at all. But, when all else failed, this is what I did and it worked.
It worked twice, even, because I was so dumb to let them get stuck twice, in two separate occasions. It worked where hot water and ice, WD-40 and oil did not.
I thought I had lost them so I decided to sacrifice one – the inner one, I decided. I wanted to break it (free). I took a burin and a mallet, I placed the steel tip onto the coffee cup stuck inside the tea mug, and I hit. I expected a crash and a crack but I simply dislodged the cup and after a few manoeuvres I freed it.
So, perhaps there was a reason I liked so much these cups: I could see they were well made and they wonderfully survived a hard hit that would break most cups.
When all else fail, try this.