The ferromagnetic state of CePdSb below 17 K has been confirmed by zero-field Sb NMR. The effective field at the Sb nucleus at low temperature is +2.78 T and the quadrupole interaction is 3.8 (2.3) MHz for . The NMR spectra do not reflect reported magnetic behaviour at 6 K. The transition at this temperature is therefore thought to be due to a second phase. The value of is , which is similar to that of . The value of , which is estimated to be times the value expected for an isotropic elastic solid. The elastic properties of CePdSb are therefore predicted to be extremely anisotropic. The temperature dependence of was measured from 1.4 - 15 K but measurements are required to lower temperatures before it can be decided whether a 4.5 K gap exists in the spin-wave spectrum, as postulated from heat capacity measurements.