  We present a semiclassical calculation of instanton effects in N=4
supersymmetric Yang-Mills theory formulated on R^{3}XS^{1} and also in the N=1
theory obtained by introducing chiral multiplet masses. In the N=4 case, these
instanton effects are related to the bulk contribution to the index which
counts BPS dyons in the corresponding four dimensional theory. In both cases,
the calculations provide semiclassical tests of recently proposed exact results
for the lowest non-trivial terms in the derivative expansion of the Wilsonian
effective action.
