Inclusive jet cross sections in photoproduction for events containing a D* meson have been measured with the ZEUS detector at HERA using an integrated luminosity of 78.6 pb-1. The events were required to have a virtuality of the incoming photon, Q2, of less than 1 GeV2, and a photon-proton centre-of-mass energy in the range 130 < Wγp < 280 GeV. The measurements are compared with next-to-leading-order (NLO) QCD calculations. Good agreement is found with the NLO calculations over most of the measured kinematic region. Requiring a second jet in the event allowed a more detailed comparison with QCD calculations. The measured dijet cross sections are also compared to Monte Carlo (MC) models which incorporate leading-order matrix elements followed by parton showers and hadronisation. The NLO QCD predictions are in general agreement with the data although differences have been isolated to regions where contributions from higher orders are expected to be significant. The MC models give a better description than the NLO predictions of the shape of the measured cross sections. © 2005 Elsevier B.V. All rights reserved.