Fun with viewpoints and rendering engines.
A few things you can do.
- Standardize on a certain set of view ports to support.
- Craft everything in percentages and Ems to allow it to flow.
- Avoid a 'rigid' design
- Split traffic to separate desktop / tablet / mobile sites, and maintain multiple sites as a result.
All major browsers offer a emulation mode which let's you adjust the screen to mimic things from a phone on up. That said, the key work is Mimic. You can emulate a Surface Pro, but that's not going to make Chrome load Spartan or Trident for rendering engines.
For the best flexibility, you're going to want a Mac. This will allow you to debug iOS devices, Android Devices, and via Virtual Machines and modern.ie mimic different Microsoft browsers. Keep in mind that the more advanced CSS may still be prefixed in some browsers, and you're going to have to account for that too.