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.
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.