Hey Steve,
If you’re trying to get the same exact output as you would get from dragging the Mini Calendar widget to a “normal” widget area, then my best recommendation here would to be create a new custom Widget Area wherever you need it in your theme.
While all the details of doing this are a bit outside the scope of our support forums here, there’s an awesome in-depth tutorial about this on the WordPress Codex → http://codex.wordpress.org/Widgetizing_Themes
If you follow the steps there to get started, you should have a widget area that you can just go back to Appearance > Widgets in your theme and drag the widget up to that new Widget Area.
Another option, which is simpler but gives you less control, and no control from the admin, is to just call the widget directly with the WordPress function called the_widget(). You can learn more about this function here → http://codex.wordpress.org/Function_Reference/the_widget
Let us know if this advice helps or if you have any other questions/concerns!
Cheers,
George