Marc,
There are a large group of tools that allow you to simulate the many different display devices that are currently in use.
The first thing that you need to determine is what browser do you normally develop in for testing? The reason that I ask is that many of the browser rendering engines have tools available for what you are looking for.
For instance, Google Chrome, which happens to be the most popular browser currently in use, has a wide variety of testing tools for developers to help them troubleshoot and test their applications before deployment. One tool that allows for different view-port sizes is Virtual View port. It is a plug in for the developers tools of Google Chrome.
Device Mode is another tool for simulating different device sizes. These are all part of the Google Developer Tool Kit. Some are plug ins that you add to the kit, others are built in by default. To access the developer tools for Google Chrome, bring up a web page and press the following keys. Ctrl-Shift-I on the PC, Cmd-SHIFT-I on the MAC.
Just Goggle "Ad-on to the google developer tools" , there are 100's of tools that are available for developers.
On a side note, most browser rendering engines have their own set of developer tool. Google Chrome is the most popular and the one that the majority of developers use. It is so popular that I actually have a 3 credit hour course that I teach in my web engineering major that is centered around the Google developer tools and how to best use them. They are pretty powerful and if used correctly can save a ton of time during development.
Quick note: There is nothing better than testing your apps on the actual devices once you get past the testing phase. As good as tools are they will never replace the actual devices as every device is slightly different and will display slightly different based on a multitude of variables with the devices.
I hope this helps.