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Magnetic shields in the form of parallel sheets were fabricated using second generation high temperature superconducting (2G HTS) materials. Shielding factor increases with addition of superconducting layers, but does not change with the increase in the interlayer separation. The result is a useful observation because large separation between the layers enhances the cooling efficiency and reduces the pressure drop for the circulation of cryogenic fluid necessary to cool the superconducting shields. Larger interlayer separation also lowers ac losses due to the self-field effects. The results suggest that the slight increase in the size of the shield due to the larger separation does not have noticeable decrease in shielding factor or the effect is compensated by the more efficient cooling. Measurements of frequency dependence indicate that the shielding factor increases with increasing frequency due to the presence of ferromagnetic substrate and a thin layer of silver on the coated conductor tapes.