In this work we investigate different approaches for calculating electric field gradients in order to provide accurate theoretical values for the nuclear quadrupole moments (NQM) for aluminum and gallium. Electron correlation is included in a fully four-component framework at the CCSD(T) level. The resulting NQM for Al-27 (146.0 +/- 0.4 mb) is in good agreement with earlier work, while the value for Ga-69 (171 +/- 2 mb) is higher than: suggested on basis of previous molecular calculations.