Using the Embed web part I was trying to paste in a site URL when I should have been using the iFrame HTML tag.
<iframe src="https://sharepointed.com" height="200" width="300"></iframe>
If you encounter this error: This website doesn’t support embedding using just the address ….
You will need to update the HTML Field Security settings in the Site Settings area of your site. In my case, I simply added sharepointed.com to the Allow iframes from this domain list, then updated the web part again.