Synchrotron X-ray, neutron powder diffraction, magnetic susceptibility, and electrical resistance measurements were used to investigate the Nd1-xCaxFeAsO series. The solubility of calcium is limited to 0 <= x <= 0.05. Within this interval, the iron arsenide layer contracts linearly in agreement with the hole doping of anti-bonding iron 3d-orbital states at the Fermi level. Depletion of the free charge carriers results in a transition to semiconducting behaviour. The iron spin-density wave (SDW) transition temperature is reduced from 140 K (x = 0) to 125 K (x = 0.025) to 130 K (x = 0.05). Long-range SDW ordering is only observed in neutron diffraction concomitant with that of the rare-earth sublattice (T-N,T-Nd approximate to 2 K), revealing that the Nd ordering enhances the ordered Fe moment in spite of the large difference in ordering temperature. The transition to semiconducting behaviour results in a dramatic change in the magnitude and Field dependence of the magnetoresistance (MR), which is much reduced (R/R-0 = 1.6 for x = 0, 1.03 for x = 0.025, and 1.06 for x = 0.05 at 5 K and in 9 Tesla) and becomes more linear for x > 0. Finally, M R is First observed at the onset of the structural P4/nnun -> Cmma transition, and increases more rapidly below T-SDW, providing further evidence that the structural phase transition and SDW are linked.