Responsive CSS Grid with persistent aspect ratio

You could take advantage of the fact that padding in percentages is based on width.

This CSS-tricks article explains the idea quite well:

...if you had an element that is 500px wide, and padding-top of 100%, the padding-top would be 500px.

Isn't that a perfect square, 500px × 500px? Yes, it is! An aspect ratio!

If we force the height of the element to zero (height: 0;) and don't have any borders. Then padding will be the only part of the box model affecting the height, and we'll have our square.

Now imagine instead of 100% top padding, we used 56.25%. That happens to be a perfect 16:9 ratio! (9 / 16 = 0.5625).

So in order for the columns to maintain aspect ratio:

1. Set the column widths as you suggested:

   grid-template-columns: repeat(auto-fit, minmax(160px, 1fr))
   

2. Add a pseudo element to the items to maintain the 16:9 aspect ratio:

   .item:before {
     content: "";
     display: block;
     height: 0;
     width: 0;
     padding-bottom: calc(9/16 * 100%);
   }
   

.grid {
  display: grid;
  grid-template-columns: repeat(auto-fit, minmax(160px, 1fr));
  grid-template-rows: 1fr;
  grid-gap: 20px;
}
.item {
  background: grey;
  display: flex;
  justify-content: center;
}
.item:before {
  content: "";
  display: block;
  height: 0;
  width: 0;
  padding-bottom: calc(9/16 * 100%);
}

<div class="grid">
  <div class="item"></div>
  <div class="item"></div>
  <div class="item"></div>
  <div class="item"></div>
  <div class="item"></div>
  <div class="item"></div>
  <div class="item"></div>
  <div class="item"></div>
  <div class="item"></div>
  <div class="item"></div>
  <div class="item"></div>
  <div class="item"></div>
  <div class="item"></div>
</div>

Codepen Demo (Resize to see the effect)

CSS Evolution : aspect-ratio property

We can now use aspect-ratio CSS4 property (Can I Use ?) to manage easily aspect ratio without padding and pseudo-element tricks. Combined with object-fit we obtain very interesting rendering.

Here, photos of various ratios I need to render in 16/9 :

section {
  display: grid;
  gap: 10px;
  grid-template-columns: repeat(auto-fill, minmax(200px, 1fr)); /* Play with min-value */
}

img {
  background-color: gainsboro; /* To visualize empty space */
  aspect-ratio: 16/9; 
  /*
    "contain" to see full original image with eventual empty space
    "cover" to fill empty space with truncating
    "fill" to stretch
  */
  object-fit: contain;
  width: 100%;
}

<section>
  <img src="https://placeimg.com/640/360/architecture">
  <img src="https://placeimg.com/640/360/tech">
  <img src="https://placeimg.com/360/360/animals">
  <img src="https://placeimg.com/640/360/people">
  <img src="https://placeimg.com/420/180/architecture">
  <img src="https://placeimg.com/640/360/animals">
  <img src="https://placeimg.com/640/360/nature">
</section>

Playground : https://codepen.io/JCH77/pen/JjbajYZ