Recently, the stochastic series expansion (SSE) has been proposed as a powerful Monte Carlo method, which allows simulations at low T for quantum-spin systems. We show that the SSE allows us to compute the magnetic conductance for various one-dimensional spin systems without further approximations. We consider various modifications of the anisotropic Heisenberg chain. We recover the Kane-Fisher scaling for one impurity in a Luttinger liquid and study the influence of noninteracting leads for the conductance of an interacting system.