We have performed electrical transport measurements at low temperatures and high magnetic fields in Na(0.5)CoO2 single crystals. Shubnikov-de Haas oscillations corresponding to only 1% of the area of the orthorhombic Brillouin zone were clearly observed, indicating that most of the original Fermi surface vanishes at the charge-ordering (CO) transition. In-plane magnetic fields were found to suppress strongly the CO state. For fields rotated within the conducting planes, we observe angular magnetoresistance oscillations whose periodicity changes from twofold to sixfold at the transition.