Can anyone recommend a graphics card which is silent and can run 2 HDMI monitors?
 
I've searched on Amazon and a couple of other sites but nothing seems to fit the bill exactly.
 
Thanks,
 
Jonesey

ATI Radeon HD 5670 could be right if you add one dvi to hdmi adapter so you get 2 hdmi:s.

Hi Jonesy,
I'm not sure what your budget is, but I just read this extensive review on this GeForce GTX 7850 ti Kalmx and it does meet your requirements: totally silent and supports 3 monitors.
 
http://www.guru3d.com/articles-pages/palit-geforce-gtx-750-ti-kalmx-review.html
 

I have a Nvidia card which is fanless - NVS450. 
it is 4 screen output though. 

New mother boards support 3 monitors now with the built in, They are dead quiet as there is no fans. You don't need much for what we do. 

How about one HDMI and one DVI-D, if one of your monitors has DVI? I installed an ASUS GT630 in my latest build for my two monitors. Fanless and a very nice heatsink. I also use my DAW for video editing and this performs very well.
Search on this and you will find it:
ASUS GT630-SL-1GD3-L Graphics card - 1 GB - GDDR3 SDRAM

I use a ATI Radeon HD 5570 and it can run up to 4 monitors (I'm running 3).  I haven't noticed any noise from it.

Thanks for all the comments/suggestions so far
 
I've done a bit of reading/research and it would appear that my motherboard, an Asus P9X79, doesn't have any ports for connecting monitors.
 
Can anyone confirm or deny this?

You're right. The Asus P9X79 doesn't have any video ports so doesn't support built-in cpu video.

Thanks Steve.