In this article, two miniaturized, dual-band, enhanced gain, flexible, low specific absorption rate (SAR) artificial magnetic conductor (AMC) integrated antennas operating at 2.4 GHz ISM and 3.9 GHz WiMAX bands have been proposed. Two compact monopoles with defected stepped ground structures have been used to improve the radiation characteristics while integrated with a common AMC surface. Defected dumbbell shaped unit-cell has been designed to obtain zero reflection phase and modify the material features. The capacitive effect of the AMC along with the defected stepped ground structures of the monopoles have excited two resonating bands and miniaturized the antennas. Proposed AMC has compensated the out-of-phase radiation toward main beam direction to increase the gain up to 8.6 dB, which is 85% more than that of the only monopole. The AMC has enhanced the reflectance exploiting the double-negative property and made the emitted radiation more directives. The integrated antennas have bestowed robust impedance matching in various bent condition by virtue of in phase reflection property. SAR values have been suppressed significantly up to 0.021 W/kg at a distance 5 mm from the human body, which is 99.5% better than that of the monopole alone