Congruence between host and parasite phylogenies is often taken as evidence for cospeciation. However, 'pseudocospeciation', resulting from host-switches followed by parasite speciation, may also generate congruent trees. To investigate this process and the conditions favouring its appearance, we here simulated the adaptive radiation of a parasite onto a new range of hosts. A very high congruence between the host tree and the resulting parasite trees was obtained when parasites switched between closely related hosts. Setting a shorter time lag for speciation after switches between distantly related hosts further increased the degree of congruence. The shape of the host tree, however, had a strong impact, as no congruence could be obtained when starting with highly unbalanced host trees. The strong congruences obtained were erroneously interpreted as the result of cospeciations by commonly used phylogenetic software packages despite the fact that all speciations resulted from host-switches in our model. These results highlight the importance of estimating the age of nodes in host and parasite phylogenies when testing for cospeciation and also demonstrate that the results obtained with software packages simulating evolutionary events must be interpreted with caution.