NSLayoutConstraints code to center a view and maintain its aspect ratio

If you want to center the red box horizontally, then you want to equate the views' CenterX, not CenterY. So that constraint should look like this:

[NSLayoutConstraint constraintWithItem:contentView
                             attribute:NSLayoutAttributeCenterX
                             relatedBy:NSLayoutRelationEqual
                                toItem:self.view
                             attribute:NSLayoutAttributeCenterX
                            multiplier:1.f constant:0.f]];

Then on the first constraints, the constraints you have there are ambiguous since there is more than one way to satisfy >=0 margin on each side and <=400 in width. A better way would be to say exactly what you said in your question, which is that you need the width to be <=400 and you would like the margins to be 0 if possible.

So something like this:

[NSLayoutConstraint constraintsWithVisualFormat:@"H:|-(0@900)-[contentView(<=400)]-(0@900)-|"
                                        options:0 metrics:0 views:views]];

I believe that gets you want you want?