  In this work, we adapt the {\em micro-macro} methodology to stochastic
differential equations for the purpose of numerically solving oscillatory
evolution equations. The models we consider are addressed in a wide spectrum of
regimes where oscillations may be slow or fast. We show that through an ad-hoc
transformation (the micro-macro decomposition), it is possible to retain the
usual orders of convergence of Euler-Maruyama method, that is to say, uniform
weak order one and uniform strong order one half. We also show that the same
orders of uniform accuracy can be achieved by a simple integral scheme. The
advantage of the micro-macro scheme is that, in contrast to the integral
scheme, it can be generalized to higher order methods.
