Making a Viewbox scale vertically but stretch horizontally

There is no such control include with WPF but you can write one yourself without too much trouble. Here is a custom ViewboxPanel that has your specifications:

public class ViewboxPanel : Panel
{
    private double scale;

    protected override Size MeasureOverride(Size availableSize)
    {
        double height = 0;
        Size unlimitedSize = new Size(double.PositiveInfinity, double.PositiveInfinity);
        foreach (UIElement child in Children)
        {
            child.Measure(unlimitedSize);
            height += child.DesiredSize.Height;
        }
        scale = availableSize.Height / height;

        return availableSize;
    }

    protected override Size ArrangeOverride(Size finalSize)
    {
        Transform scaleTransform = new ScaleTransform(scale, scale);
        double height = 0;
        foreach (UIElement child in Children)
        {
            child.RenderTransform = scaleTransform;
            child.Arrange(new Rect(new Point(0, scale * height), new Size(finalSize.Width / scale, child.DesiredSize.Height)));
            height += child.DesiredSize.Height;
        }

        return finalSize;
    }
}

and you use it like this:

<local:ViewboxPanel>
    <Button>Foo</Button>
    <Button>Bar</Button>
</local:ViewboxPanel>

It definitely needs some work but this might get you started.

To keep width to work correctly:

protected override Size MeasureOverride(Size availableSize)
    {
        double height = 0;
        Size unlimitedSize = new Size(double.PositiveInfinity, double.PositiveInfinity);
        foreach (UIElement child in Children)
        {
            child.Measure(unlimitedSize);
            height += child.DesiredSize.Height;
        }
        scale = availableSize.Height / height;

        foreach (UIElement child in Children)
        {
            unlimitedSize.Width = availableSize.Width / scale;
            child.Measure(unlimitedSize);
        }           

        return availableSize;
    }