What PCB electromagnetic simulation tools are available?
crunchyard.com offers cloud-based renting of CPU time which includes, as an option, Feko. You pay for VM/hour and the prices are quite reasonable.

You can download a free trial of Feko at their website which is unrestricted for 45 days (requires a login registration). There's also a free Lite version that you can use without time restrictions (you just need to ask for a license) but it has stringent limitations to simulation complexity. One thing you could do is use the Lite version to create/edit your model and then rent time at Crunchyard to run the simulation.

The Trial and Lite versions include good instructional videos for the basics of using Feko. But, as Kortuk said, it's laborious to recreate the PCB in it. One alternative you have is to import other CAD formats like DXF, provided your PCB design software supports it. But you're obviously importing just the geometry, not the EM profile of the traces. Those AFAIK you'll have to setup by hand.
By reading Feko manual it appears that when importing Parasolid files it'll recognize special attributes of the objects that may contain EM characteristics, but I never tried it. You'd need a PCB software that can export that format and also be able to read those characteristics from somewhere (the schematics perhaps).

This is the simulation result for a simple PCB rectangular surface area.