How to set UILabel only width and height and constraints programmatically

To create label with height and width constraints here is the constraints...And don't forget to add label in to view with addSubview method

UILabel *Label = [[UILabel alloc] init];
[Label setTranslatesAutoresizingMaskIntoConstraints:NO];  

[self.view addSubview:Label];

// Width constraint
[Label addConstraint:[NSLayoutConstraint constraintWithItem:Label
                                                      attribute:NSLayoutAttributeWidth
                                                      relatedBy:NSLayoutRelationEqual
                                                         toItem:nil
                                                      attribute: NSLayoutAttributeNotAnAttribute
                                                     multiplier:1
                                                       constant:200]];

// Height constraint
[Label addConstraint:[NSLayoutConstraint constraintWithItem:Label
                                                      attribute:NSLayoutAttributeHeight
                                                      relatedBy:NSLayoutRelationEqual
                                                         toItem:nil
                                                      attribute: NSLayoutAttributeNotAnAttribute
                                                     multiplier:1
                                                       constant:21]];

Swift 4:

label.translatesAutoresizingMaskIntoConstraints = false
label.addConstraint(NSLayoutConstraint(item: label, attribute: .height, relatedBy: .equal, toItem: nil, attribute: .notAnAttribute, multiplier: 1, constant: 21))
label.addConstraint(NSLayoutConstraint(item: label, attribute: .width, relatedBy: .equal, toItem: nil, attribute: .notAnAttribute, multiplier: 1, constant: 200))

And In Swift

 Label.setTranslatesAutoresizingMaskIntoConstraints(false)
 self.view.addSubview(Label)

 Label.addConstraint(NSLayoutConstraint(item: Label, attribute: .Height, relatedBy: .Equal, toItem: nil, attribute: .NotAnAttribute, multiplier: 1, constant: 21))
 Label.addConstraint(NSLayoutConstraint(item: Label, attribute: .Width, relatedBy: .Equal, toItem: nil, attribute: .NotAnAttribute, multiplier: 1, constant: 200))  

Check this link for more detail

UPDATE
As you update your question, here is my updated answer...

UILabel *Label1 = [[UILabel alloc] init];
[Label1 setTranslatesAutoresizingMaskIntoConstraints:NO];
UILabel *Label2 = [[UILabel alloc] init];
[Label2 setTranslatesAutoresizingMaskIntoConstraints:NO];

Label1.text = @"Label1";
Label1.backgroundColor = [UIColor blueColor];
Label2.text = @"Label2";
Label2.backgroundColor = [UIColor redColor];

[self.view addSubview:Label1];
[self.view addSubview:Label2];

// Width constraint
[Label1 addConstraint:[NSLayoutConstraint constraintWithItem:Label1
                                                  attribute:NSLayoutAttributeWidth
                                                  relatedBy:NSLayoutRelationEqual
                                                     toItem:nil
                                                  attribute: NSLayoutAttributeNotAnAttribute
                                                 multiplier:1
                                                   constant:280]];

// Height constraint
[Label1 addConstraint:[NSLayoutConstraint constraintWithItem:Label1
                                                  attribute:NSLayoutAttributeHeight
                                                  relatedBy:NSLayoutRelationEqual
                                                     toItem:nil
                                                  attribute: NSLayoutAttributeNotAnAttribute
                                                 multiplier:1
                                                   constant:21]];

// CenterX constraint
[self.view addConstraint:[NSLayoutConstraint constraintWithItem:self.view
                                                   attribute:NSLayoutAttributeCenterX
                                                   relatedBy:NSLayoutRelationEqual
                                                      toItem:Label1
                                                   attribute: NSLayoutAttributeCenterX
                                                  multiplier:1
                                                    constant:0]];
// Top constraint
[self.view addConstraint:[NSLayoutConstraint constraintWithItem:Label1
                                                      attribute:NSLayoutAttributeTop
                                                      relatedBy:NSLayoutRelationEqual
                                                         toItem:self.topLayoutGuide
                                                      attribute: NSLayoutAttributeBottom
                                                     multiplier:1
                                                       constant:40]];


// label2
[self.view addConstraint:[NSLayoutConstraint constraintWithItem:Label1
                                                      attribute:NSLayoutAttributeLeading
                                                      relatedBy:NSLayoutRelationEqual
                                                         toItem:Label2
                                                      attribute: NSLayoutAttributeLeading
                                                     multiplier:1
                                                       constant:0]];
// label2.Height = label1.Height
[self.view  addConstraint:[NSLayoutConstraint constraintWithItem:Label1
                                                      attribute:NSLayoutAttributeHeight
                                                      relatedBy:NSLayoutRelationEqual
                                                         toItem:Label2
                                                      attribute: NSLayoutAttributeHeight
                                                     multiplier:1
                                                       constant:0]];
// label2.width = label1.width
[self.view  addConstraint:[NSLayoutConstraint constraintWithItem:Label1
                                                   attribute:NSLayoutAttributeWidth
                                                   relatedBy:NSLayoutRelationEqual
                                                      toItem:Label2
                                                   attribute: NSLayoutAttributeWidth
                                                  multiplier:1
                                                    constant:0]];

// label2.Top
[self.view addConstraint:[NSLayoutConstraint constraintWithItem:Label2
                                                      attribute:NSLayoutAttributeTop
                                                      relatedBy:NSLayoutRelationEqual
                                                         toItem:Label1
                                                      attribute: NSLayoutAttributeBottom
                                                     multiplier:1
                                                       constant:34]];  

Result Screen

i try this method to change height as text length in your label.

put viewdidload

[yourlabel setNumberOfLines:0];
    CGRect mainframe = _lbl_board.frame;
    mainframe.size.height =  [self getLabelHeight:yourlabel];
    yourlabel.frame = mainframe;

method

- (CGFloat)getLabelHeight:(UILabel*)label
{
    CGSize constraint = CGSizeMake(label.frame.size.width, CGFLOAT_MAX);
    CGSize size;

    NSStringDrawingContext *context = [[NSStringDrawingContext alloc] init];
    CGSize boundingBox = [label.text boundingRectWithSize:constraint
                                                  options:NSStringDrawingUsesLineFragmentOrigin
                                               attributes:@{NSFontAttributeName:label.font}
                                                  context:context].size;

    size = CGSizeMake(ceil(boundingBox.width), ceil(boundingBox.height));

    return size.height;
}