David Woolley wrote:

The quiet sun component of the microwave noise at the earth, at about
1.4Ghz, is about 5E-21 watts / square metre / Hz (5E5 Janskies).  The Sun
is about 1.5E11 metres away, so the illuminated surface is 4 pi times
the square of this (2.83E23 square metres) giving a total isotropic
power output of about 1,400 watts per Hz.  Over the 0.1Hz of a stable
carrier subject to the Drake-Helou limit, that is 140 watts.  (Note
this is a lot more than 10E10 watts integrated over any reasonable
definition of the whole microwave band.)

Thanks for the info. As I already mentioned, I meant a 
transmitter which radiates microwaves in all directions,
like the Sun. Surprisingly, my rough estimate is not far
away from yours -- it would take a 1 kW microwave transmitter
to outshine the Sun. The problem is that this transmitter
cannot outshine the cosmic microwave background radiation.
Making a narrow, high intensity microwave beam does not
make sense because nobody knows where and when to aim
the beam. A non-directional transmitter would have to emit
infrared, visible, ultraviolet, X-ray, or Gamma radiation
to outshine the cosmic microwave background radiation.
The cheapest transmitter of this kind is probably an array
of mirrors. Alas, even the mirrors are too expensive, at
least for our civilization.