I know how to work with object of type Graphics (at least I am able to render images) but I always do that by passing graphics object retrieved from OnPaint method.
None of the preceding answers worked for me. I found Rajnikant Rajwadi solution effective (see https://social.msdn.microsoft.com/Forums/vstudio/en-US/ce90eb80-3faf-4266-b6e3-0082191793f7/creation-of-graphics-object-in-wpf-user-control?forum=wpf)
Here is a horribly condensed call to Graphics.MeasureString(). (please code more responsibly)
SizeF sf = System.Drawing.Graphics.FromHwnd(new System.Windows.Interop.WindowInteropHelper(this).Handle).MeasureString("w", new Font(TheControl.FontFamily.ToString(), (float)TheControl.FontSize));