I have an animation that I\'m displaying using a UIImageView:
imageView.animationImages = myImages;
imageView.animationDuration = 3;
[imageView startAnimating];
This code will pause an animated object at its current position in the animation process. If you record other variables like the time or progress or whatever you need, it should be fairly trivial to resume the animation again.
UIView *viewBeingAnimated = //your view that is being animated
viewBeingAnimated.frame = [[viewBeingAnimated.layer presentationLayer] frame];
[viewBeingAnimated.layer removeAllAnimations];
//when user unpauses, create new animation from current position.