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We show how the combination of string method with the phase-field approach can be extended from simulations of homogeneous nucleation to heterogeneous nucleation. From these simulations, it is possible to directly obtain nucleation barriers for heterogeneous nucleation on arbitrary surfaces as well as information about the size and shape of the critical nucleus. We test the method by comparing the dependence of the nucleation barrier for heterogeneous nucleation on concave and convex surfaces on the surface curvature obtained from three-dimensional phase-field simulations with predictions from classical nucleation theory and find good agreement between them.