The way I did it was to download/installed Fiddler (http://www.fiddlertool.com/) which is an inspecting proxy. I followed the instructions to enable https decryption, and told Windows to trust the fiddler root certificate (Moved from Personal->Certificates to Trusted Root Certificate Authorities->Certificates).
Checked IE worked and it was fine, then I modified the application.exe.config file under the Docs and Settings\user\Local Settings\Application Data\Vendor\App and added
<configuration>
<system.net>
<defaultProxy>
<proxy proxyaddress="http://localhost:8888" />
</defaultProxy>
</system.net>
</configuration>
I thought I was being very clever, but it turns out I couldn't get it to work. So I switched to using HTTPS instead.
Fiddlertool is pretty cool though :)