The pure rotational spectrum of CaNH2 in its (X) over bar (2)A(1) ground electronic state has been recorded using millimeter/submillimeter direct absorption methods in the frequency range 320-537 GHz as well as that of CaND2. The species were created by Broida-oven techniques. Eleven rotational transitions were observed arising from the upsilon = 0 and upsilon(6) = 1 states of CaNH2, and eight transitions were recorded for the upsilon(3) = 1 and upsilon(4) = 1 levels. For CaND2, eight transitions (upsilon = 0) were also measured. For the majority of these transitions, K-a doublets corresponding to K-a = 0-5 were observed and fine structure splittings were resolved in every component. These spectra were analyzed using an S-reduced Hamiltonian; rotational, centrifugal distortion, and spin-rotation parameters were determined for CaNH2, CaND2, and the three observed vibrationally excited states. An r(0) structure has also been calculated. The data are consistent with calcium amide being a planar molecule with C-2v symmetry and having predominately ionic bonding, as indicated by previous optical studies.