Presuming you have an ellipse/circle and wish to frame it with a rectangle, and possibly to turn the rectangle into a Crop Area, you may:
0) If the ellipse/circle is bound by a stroke, turn on Edit>Preferences>General>Preview Bonds;
1) Select the ellipse/circle and create a rectangle, DoubleClicking the Rectangle Tool and inserting the W and H values from the Transform palette/panel;
2) Select both rectangle and ellipse/circle, Click the ellipse/circle once more, and Click Horizontal Align Center and Vertical Align Center in the Align palette/panel.
You may use slightly larger W and H values, and remember to turn off Preview Bonds if used. Both the Crop Area and the artwork should fit inside whole pixels.
Try this see if it suits you.
Copy and paste the ellipse either in the front or back. While the copy is still selected go to Effects>Convert to Shape>Rectangle.
Give it a relative setting of 0 for both dimensions.
Then if you wish you can give it a crop mark effect or if in CS 4 expand the appearance of the rectangle effect and ungroup and then convert to aan artboard.
Object>Convert to Artboard.
The good thing about this is you can use the width of the stroke to get the to align to the object so the object sits inside and touching the frames interior wall so to speak.
If you want to convert to an artboard then you give it half the width of the stroke as the extra amount and when the frame is converted to and artboard it will like wise be arranged.
You can as I now realize do this with just one copy of the ellipse by simply adding a new stroke and applying the convert shape effect to that stroke.
If you don't want the strokes you can always remove them later.