Update (for UWP)

In UWP Apps you don’t need this and can use the TextBlock property MaxLines (see MSDN)

Original Answer:

If you have a specific LineHeight you can calculate the maximum height for the TextBlock.

Example:

TextBlock with maximum 3 lines

<TextBlock 
  Width="300"
  TextWrapping="Wrap" 
  TextTrimming="WordEllipsis" 
  FontSize="24" 
  LineStackingStrategy="BlockLineHeight"
  LineHeight="28"
  MaxHeight="84">YOUR TEXT</TextBlock>

This is all that you need to get your requirement working.

How to do this dynamically?

Just create a new control in C#/VB.NET that extends TextBlock and give it a new DependencyProperty int MaxLines.

Then override the OnApplyTemplate() method and set the MaxHeight based on the LineHeight * MaxLines.

That’s just a basic explanation on how you could solve this problem!