Internet Explorer only works on Windows, there is no version that ever ran on any other OS. You can, however, fake out websites that look specifically for IE by using a User Agent Switcher extension in Safari or Chrome.
This, however, only addresses websites that do a cursory check (a silly and archaic thing from the stone ages of the Web) to ensure that you are using a "safe" browser.
However, if the features you are trying to use are things like ActiveX controls or other things that only work within the IE browser on Windows, then you might not have a lot of choices.
The first thing you can try is to run IE within Winebottler on Mac, this will not install Windows on your Mac, but give you the ability of running IE on it. See the instructions here:
How to Install Internet Explorer on Mac Using WineBottler. If this works, great.
If the previous step doesn't work and you HAVE to use this website, then you might have no choice but to go down the Virtualization route and run a version of Windows with IE on it to access this website.