To make an embed HTML tag responsive, you can use CSS to set the `width` and `height` properties to `100%` and the `max-width` to the original width of the embedded content. This will ensure that the content scales down to fit smaller screen sizes, while still maintaining its original aspect ratio.

Here is an example of how you could do this:

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In this example, we use a `div` element with the class `responsive-embed` to wrap the `iframe` that contains the embedded content. We then use CSS to set the `width` and `height` of the `iframe` to `100%`, and the `max-width` to the original width of the content. This ensures that the content scales down to fit smaller screens, while maintaining its original aspect ratio.