How to use web.config authentication to build an administrator-only page when UAC is enabled?

Question

I'm building a page that should only be visible to administrators on the web server. The standard prescription for this is:

<system.web>
  <identity impersonate="true" />
  <authorization>
    <allow roles="BUILTIN\Administrators" />
    <deny users="*" />
  </authorization>
</system.web>

but when User Access Control (UAC) is enabled on the server, ASP.NET pretends that no users are in the Administrators group. Even when I impersonate a user, that user's list of groups does not include the Administrators group.

How then should I be adding this kind of security to my page?