We investigated antidot lattices with Andreev reflecting boundaries both in experiment and theory. The samples consist of arrays of niobium-filled antidots in an InAs-based heterostructure. The quality of the Nb–InAs contact could be controlled by an in situ Ar+ sputter cleaning step. In samples with a high transparency contact, we find a strong reduction of the resistance around B=0 and a suppression of the commensurability peaks. These observations can be explained in a classical Kubo approach by including Andreev reflection and assuming a magnetic-field-dependent Andreev reflection probability.