You can use ST_Envelope to get the extents of a bounding box around some feature, in, the minimum bounding rectangle (MBR).
select ST_Astext(ST_Envelope(ST_Buffer(ST_Makepoint(0,0),10)));
returns a rectangle not a circle
POLYGON((-10 -10,-10 10,10 10,10 -10,-10 -10))
You can then use the min and max functions, ST_Xmax, ST_Xmin and the Y equivalents to get the width, height of the MBR.
Is this what you asked?