Frame frame = new Frame();
frame.addComponentListener(new ComponentAdapter()
{
    @Override
    public void componentResized(ComponentEvent e)
    {
        Component c = (Component)e.getSource();
        Dimension newSize = c.getSize();

        frame.setSize(newSize.getWidth(), newSize.getWidth() / 2);
    }
});

Dim OldWidth As Double = 600
Dim NewWidth As Double
Dim OldHeight As Double = 300
Dim NewHeight As Double

Private Sub Form1_ResizeBegin(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.ResizeBegin
        OldWidth = Me.Width
        OldHeight = Me.Height
End Sub

Private Sub Form1_SizeChanged(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.SizeChanged
        NewWidth = Me.Width
        NewHeight = Me.Height

        If NewHeight <> OldHeight Then
            NewWidth = (NewHeight * OldWidth) / OldHeight
            Me.Width = CInt(NewWidth)
        End If
        If NewWidth <> OldWidth Then
            NewHeight = (NewWidth * OldHeight) / OldWidth
            Me.Height = CInt(NewHeight)
        End If
End Sub