Some good information from a Chilkat customer:
It turns out the problem was that we were using a Visual Studio Web Site project type. Instead of this, we found that using a Visual Studio Web App project type works. A “site” runs in some whimpy web server on the developer machine that is only 32-bit, something called Cassini, but some people adamantly declare it’s not *really* Cassini… Whatever, I have no tolerance for any web server on my development machine that cannot run in 64-bit whether it is the real Cassini or not! Ha! So anyway, we created a new Web App project and then you get a ton of options that allow you to specify the target processor platform, etc. We set everything to x64, and then we configured the Web App to use the REAL IIS 8.0 web server on my 64-bit machine, connecting to a real IIS Application, and then everything works. Of course, we need to run Visual Studio with elevated permissions in order to debug but that is just fine with us.
So the moral of the story is… If you want 64-bit on a development machine, use a Web App project, not a Web Site project!