We present a theoretical study of intergalactic metal absorption lines imprinted in the spectra of distant quasars during and after the Epoch of Reionization (EoR). We use high resolution hydrodynamical simulations at high redshift ($4 <z<8$), assuming a uniform UV background Haardt--Madau 12, post-processing with CLOUDY photoionization models and Voigt profile fitting to accurately calculate column densities of the ions CII, CIV, SiII, SiIV and OI in the intergalactic medium (IGM). In addition, we generate mock observations of neutral Hydrogen (HI) at $z<6$. Our simulations successfully reproduce the evolution of the cosmological mass density ($\Omega$) of CII and CIV, with $\Omega_{CII}$ exceeding $\Omega_{CIV}$ at $z >6$, consistent with the current picture of the tail of the EoR. The simulated CII exhibits a bimodal distribution with large absorptions in and around galaxies, and some traces in the lower density IGM. We find some discrepancies between the observed and simulated column density relationships among different ionic species at $z=6$, probably due to uncertainties in the assumed UV background. Finally, our simulations are in good agreement with observations of the HI column density distribution function at $z = 4$ and the HI cosmological mass density $\Omega_{HI}$ at $4 < z < 6$.