Electrically conductive objects can be detected using the principle of electromagnetic induction, where a primary oscillating magnetic field induces eddy currents in the object, which in turn produce a secondary magnetic field that can be measured with a magnetometer. We have developed a portable radio-frequency optically pumped magnetometer (RF OPM) working in unshielded conditions with sub-pT/Hz magnetic field sensitivity when used for the detection of small oscillating magnetic fields, setting a new benchmark for the sensitivity of a portable RF OPM in unshielded conditions. Using this OPM, we have detected the induced magnetic field from aluminum disks with diameters as small as 1.5 cm and with the disks being ∼25 cm from both the excitation coil and the magnetometer. When used for eddy current detection, our magnetometer achieves a sensitivity of a 2-6 pT/Hz. We have also detected a moving aluminum disk using our RF OPM and analyzed the magnetometer signals, which depend on the position of the disk, illustrating the potential of high sensitivity RF OPMs for remote sensing applications.