A systematic method for building an extensible tight-binding model from ab initio calculations has been developed and tested on two hexagonal metals: Zr and Mg. The errors introduced at each level of approximation are discussed and quantified. For bulk materials, using a limited basis set of spd orbitals is shown to be sufficient to reproduce with high accuracy bulk energy versus volume curves for fcc, bcc, and hcp lattice structures, as well as the electronic density of states. However, the two-center approximation introduces errors of several tenths of eV in the pair potential, crystal-field terms, and hopping integrals. Environmentally dependent corrections to the former two have been implemented, significantly improving the accuracy. Two-center hopping integrals were corrected by taking many-center hopping integrals for a set of structures of interest, rotating them into the bond reference frame, and then fitting a smooth function through these values. Finally, a pair potential was fitted to correct remaining errors. However, this procedure is not sufficient to ensure transferability of the model, especially when point defects are introduced. In particular, it is shown to be problematic when interstitial elements are added to the model, as demonstrated in the case of octahedral self-interstitial atoms.