browserstack.com
and other various testing suites can be useful.
You can also get software which syncs your dev website + user actions on said website over a series of devices - so you can see everything at once. #allTheScreens

Testing How It is Seen

There's no automated way to do this. "How responsive" depends on your work. However, apart from @Bridget's answer, you can also use Selenium to automate screenshooting of URLs of your web application. Then you can review the screenshots.

Currently, you can automate Selenium with Chrome and Firefox headlessly (without GUI). So, at least, you can check how your front-end looks for both Gecko and Chromium renderer.

Testing How It Acts

If you wonder about how it acts, then you can also use Selenium to automate browsing, like clicking buttons, selecting stuff and then assert the presence, visibility or any property of a DOM element.

Try the following tools:

• Responsinator
• Google Mobile Friendly

Google's chrome has a built in responsible tool so you can check against responsiveness , there are also a few tools online

Would something like this help?