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Go to the website. Click on the Site Preferences inspector button, which is just to the right of the Google search field in the toolbar (by default). Click on Preferences for <domain name>, Other, and then set the Identify to web servers and scripts as: choice to whatever you want.

Note that if "please use Internet Explorer" is really code for "we use that ActiveX crap in our website because we are losers" then you aren't going to get appreciably farther even if you identify as IE.