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Shielding of magnetic fields (magnetic shielding) by rare earth-based REBCO coated conductors with a highly oriented superconducting layer was measured. The shielding of magnetic fields was measured using a Hall effect sensor installed between bundles consisting of commercial REBCO conductors 12 mm in width. Measurements of the shielding of magnetic fields by other commercial high-Tc superconductors were performed for comparison. The shielding of magnetic fields was found to depend on the number of conductors in the bundle and the route of the applied magnetic fields and was observed even for fields over 10 T. In steady magnetic fields, a temporal change in the shielding of magnetic fields, that is, a decay of shielding currents induced in conductors against applied magnetic fields, was measured. The temporal change of the shielding of magnetic fields exhibited the behavior typical of high-Tc superconductors, as explained by the flux creep model. Remanent magnetic fields measured in the experiments of the shielding of magnetic fields suggest that the bundle can be used as a magnet. A quasi-bulk magnet consisting of 100 Zr-doped Zr:REBCO conductors could hold over 3 T at 4.2 K.