  A Ginsparg-Wilson based calibration of the topological charge is used to
calculate the renormalization constants which appear in the field-theoretical
determination of the topological susceptibility on the lattice. A systematic
comparison is made with calculations based on cooling. The two methods agree
within present statistical errors (3%-4%). We also discuss the independence of
the multiplicative renormalization constant Z from the background topological
charge used to determine it.
