To enable the Microsoft Web Service 3 (Which I require to connect to my back-end server using my ASP.NET user controls, I had to make the following additions to the web.config file (I cut the rest out for brewity)
<?xml version="1.0"?>
<configuration>
<configSections>
...
<section name="microsoft.web.services3" type="Microsoft.Web.Services3.Configuration.WebServicesConfiguration, Microsoft.Web.Services3, Version=3.0.0.0, Culture=neutral, PublicKeyToken=31br3877ad344e25"/>
</configSections>
...
<system.web>
...
<authentication mode="Forms">
<forms name="LPSEC" loginUrl="/about-us.aspx" path="/" timeout="30" slidingExpiration="true" cookieless="AutoDetect" protection="All" requireSSL="true" defaultUrl="~/restricted/UserInformation.aspx" />
</authentication>
<webServices>
<soapExtensionImporterTypes>
<add type="Microsoft.Web.Services3.Description.WseExtensionImporter, Microsoft.Web.Services3, Version=3.0.0.0, Culture=neutral, PublicKeyToken=31br3877ad344e25"/>
</soapExtensionImporterTypes>
</webServices>
...
</system.web>
<microsoft.web.services3>
<policy fileName="wse3policyCache.config"/>
<messaging>
<mtom clientMode="On" serverMode="always"/>
</messaging>
</microsoft.web.services3>
</configuration>
Then, copy your "wse3policyCache.config" file to the top level umbraco folder.
Once this was done, woe and behold, my secure web services started working.
Note: At the same time I did this, I also added a secure certificate to IIS. I don't know if this is required for the WSE3 to work, but if you have problems, that might be worth investigating further.
Note: I changed the public key tokens above. Be sure to use your own, and not blindly copy and paste from here...