I didn't have luck with any of these suggestions. My string contained unicode bullet points and I suspect they were causing grief in the calculation. I noticed UITextView was handling the drawing fine, so I looked to that to leverage its calculation. I did the following, which is probably not as optimal as the NSString drawing methods, but at least it's accurate. It's also slightly more optimal than initialising a UITextView just to call -sizeThatFits:
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NSTextContainer *textContainer = [[NSTextContainer alloc] initWithSize:CGSizeMake(width, CGFLOAT_MAX)];
NSLayoutManager *layoutManager = [[NSLayoutManager alloc] init];
[layoutManager addTextContainer:textContainer];
NSTextStorage *textStorage = [[NSTextStorage alloc] initWithAttributedString:formattedString];
[textStorage addLayoutManager:layoutManager];
const CGFloat formattedStringHeight = ceilf([layoutManager usedRectForTextContainer:textContainer].size.height);