The answer is [view layoutIfNeeded].
Here’s why:
You still get the view’s current width and height by inspecting view.bounds.size.width and view.bounds.size.height (or the frame, which is equivalent unless you’re playing with the view.transform).
If what you want is the width and height implied by your existing constraints, the answer is not to inspect the constraints manually, since that would require you to re-implement the entire constraint-solving logic of the auto layout system in order to interpret those constraints. Instead, what you should do is just ask auto layout to update that layout, so that it solves the constraints and updates the value of view.bounds with the correct solution, and then you inspect the view.bounds.
How do you ask auto layout to update the layout? Call [view setNeedsLayout] if you want auto layout to update the layout on the next turn of the run loop.
However, if you want it to update the layout immediately, so you can immediately access the new bounds value later within your current function, or at another point before the turn of the run loop, then you need to call [view setNeedsLayout] and [view layoutIfNeeded].
You asked a second question: “how can I change a height/width constraint if I don’t have a reference to it directly?”.
If you create the constraint in IB, the best solution is to create an IBOutlet in your view controller or your view so you do have a direct reference to it. If you created the constraint in code, then you should hold onto a reference in an internal weak property at the time when you created it. If someone else created the constraint, then you need to find it by examining the examining the view.constraints property on the view, and possibly the entire view hierarchy, and implementing logic which finds the crucial NSLayoutConstraint. This is probably the wrong way to go, since it also effectively requires you to determine which particular constraint determined the bounds size, when there’s not guaranteed to be a simple answer to that question. The final bounds value could be the solution to a very complicated system of multiple constraints, with multiple priorities, etc., so that no single constraint is the “cause” of the final value.