Microsoft has a tool just for this purpose: Microsoft Expression Web. There's a free version with a bunch of FrontPage/Dreamweaver-like garbage that nobody wants. What's important is that it has a great browser testing feature. I'm running Windows 8.1 Pro (final release, not preview) with Internet Explorer 11. I get these local browsers:
Then I get a Remote Browsers (Beta) option. I'm supposed to sign up with a valid e-mail, but there's an error communicating with the server. Oh well.
Firefox used to be supported, but I don't see it now. Might be hiding.
I can compare side-by-side between browser versions. I can also compare with an image, or apparently, a PSD file (no idea how well that works). InDesign would be nice, but that's probably asking for too much.
I have the full version of Expression partially installed as well due to Visual Studio Ultimate being on the same computer, so I'd appreciate someone confirming in a comment that my free installation isn't automatically upgrading.
Update: Looks like the online service was discontinued, but local browsers are still supported. You can also download just SuperPreview, without the editor garbage. If you want the full IDE, the latest version is Microsoft Expression Web 4 (Free Version). Here's the official list of supported browsers. IE6 seems to give an error on Windows 8.1, but IE7 works.
Update 2014-12-09: Microsoft has pretty much given up on this. Don't expect it to work well.