Both browsers have the ability to display content in their respective caches--temporarily saved webpage data--instead of the live version of the site.
This can be imperfect since the page can change while you're offline, rendering the saved version inaccurate, and the browser cache only contains a limited amount of your recent browsing history. It also doesn't work on sites that provide live feeds of content, such as Facebook or Netflix.
Nevertheless, if you need information from a news item or another site you were just viewing, try one of these solutions.
Chrome's method to display stale (not live) webpages is currently experimental. By default Chrome can show some webpages when offline, but with this setting enabled the feature is far more robust.
To get ready for offline mode in Chrome type chrome://flags/#show-saved-copy in the URL address bar. Then select Enable: Primary from the dropdown menu under the Enable Show Saved Copy Button heading.
Once that's done, restart your browser for the feature to take effect.
To test viewing a cached page, take your PC offline and open a webpage from your recent browsing history. You should see Chrome's typical offline error message--except now you'll also see a Show saved copy button as pictured above. Click that button and you'll see the version of the webpage as it was when you were last online.
In my tests, Chrome's cache would only show you saved copies of sites going back about a half an hour. However, that was during my work day, when I view an enormous amount of web content. Your experience may vary.
There's no special flag to set in Firefox in order to view content offline. Instead, to view pages from your cache click on the menu "hamburger" icon in the upper right corner. Then select Developer > Work Offline. Now Firefox will display the page you want as long as it's in the browser's cache.
That's all there is to viewing cached webpages offline. It's not a perfect solution, but in a pinch knowing these tricks can come in really handy.
[h/t to LifeHacker for inspiring the idea for this post]