I know a few non-Emirati women who are married to Emirati men and then are by default Emirati citizens. (My apologies if I have oversimplified this. I welcome any corrections in the comments.) However, I didn't know any native Emirati women married to non-Emirati men. I've asked about this a few times, but never really got a satisfactory answer. I was under the impression that it just didn't happen.
The National has written two articles about this, dispelling my preconceptions. As it turns out, Emirati women marrying non-Emiratis is on the rise. (This article gives details of the trend.) Unfortunately, for the women involved, they lose citizenship as do their future children. The thinking behind this is that "they are viewed as incapable of making decisions effectively, and in need of protection so as not to be taken advantage of by others.”
In a second article, an Emirati woman tells her story of marrying a Scottish-Egyptian man. She expresses her very real concerns about her desire to pass on her culture to her children despite them not being Emirati citizens. She goes on to talk about the lack of equality between Emirati men and women with regards to with international marriages.
This seems to be a law that is on the verge of change as most people mentioned in the article don't have any strong feelings in support of it. The bureaucracy regarding international marriages in the UAE make marriage in Japan seem free and easy.