The giant magnetoimpedance (GMI) and giant magnetoresistance (GMR) of amorphous ribbon/Cu/amorphous ribbon trilayer microstructures, based on Metglas(TM) 2714a ribbons and Cu foils, is measured and analyzed. We obtain GMI and GMR ratios of 830% and 2630%, respectively, in the 0.2-20 MHz frequency range. These very large GMI and GMR values are a direct consequence of the large effective relative permeability due to the closed magnetic flux path in the trilayer structure. We study the effect of magnetocrystalline and shape anisotropy, and analyze our experimental results in terms of the model of Makhnovskiy [Sens. Actuators 81, 91 (2000)].