One way that I know is using of some external libraries like Intraweb.
I tested their technology - here is result:
http://resellmyapartment.com
You can use C++ or Pascal. If you use C++Builder or Delphi, you will get Intraweb in your package without additional payment for it.
Also you will be able to compile your project like .exe application or dll extension for IIS, even it is possible using of page mode.
Also for simple tasks you can compile your project like CGI exe or dll.
There is similar technologies, you can make some google search.
For Microsoft VS the trivial way is using of C# and ASP. But have not big experience with their technology at now.
I'm not sure that understood your question correctly. If you want only any web control integration in your api, so you can using of some ActiveX browser control.