You could do something like this by calling the GetDescendant method off the control's UIElement, passing in typeof(ScrollBarUIElement), but I would advise against this for performance reasons.

The UltraFormattedTextEditor control utilizes the FormattedLinkEditor embeddable editor, and classes that derive from EmbeddableEditorBase (as FormattedLinkEditor does) expose a GetSize method, which I believe will give you the size  required to render the value. You can get a reference to the editor by calling GetDescendant off the control's UIElement, passing in typeof(FormattedLinkEmbeddableUIElement). The UIElement returned exposes an Editor property, which exposes a GetSize method. One of those overloads takes the maxWidth, to which you should pass the control's width minus borders. You might have to fudge the value a little to make sure no scrollbars appear but I think this approach would be more performant than increasing the size until the scrollbars disappear.