I'm surprised this has not been mentioned yet, but the simplest way to do this would be by setting the height, margin (and width, if you want) using viewport sizes.
As you might know, total height of the viewport = 100vh.
Say you want the height of you container to occupy 60% (60vh) of the screen, you can divide the rest (40vh) equally between the top and the bottom margin so that the element aligns itself in the centre automatically.
Setting the margin-left and margin-right to auto, will make sure the container is centred horizontally.
.container {
width: 60vw; /*optional*/
height: 60vh;
margin: 20vh auto;
background: #333;
}