In this paper, an optimized circularly polarized (CP) antenna is proposed for operating in the LTE bands 42/43 applications. This CP antenna comprises three sections, the meander-line and L-shaped strip structures modeled on the front side of a Roger 3003 substrate, and on the back side a rotated H-shaped ground plane is printed. In order to further increase the antenna common bandwidth (CBW), that is the voltage standing wave ratio bandwidth (VRBW) and axial ratio bandwidth (ARBW), an offset-fed line on the front side and a shorting pin are used. A feasible solution of the optimized CP antenna with compact size is achieved by applying an optimization design methodology with a fitness function that takes into account the antenna performance parameters, CBW, or both the VRBW and ARBW in addition to the realized gain (RG). Two programs are operating in synchronous fashion for finding the optimal geometric antenna parameters, a particle swarm optimization (PSO) for implementing the fitness function in MATLAB and a CST MWS simulator tool for extracting the antenna performance parameters. The optimized antennas without and with shorting pin are obtained with a broadest CBW and feature of CP operation and an acceptable RG across the desired LTE 42 (3.4-3.6 GHz) and LTE 42/43 (3.4-3.8 GHz) band, respectively. The proposed two designed antennas, with and without shorting pin, are fabricated, and the measured results are in good agreement with the simulated ones. From measured results, a −10 B-S 11 impedance bandwidth (IBW) of 220 and 460 MHz (3.37-3.83 GHz), a 3-dB ARBW of 200 MHz (3.4-3.6 GHz) and 390 MHz (3.42-3.81 GHz) with respective maximum RG of 2.26 and 2.39 dBic are exhibited by the antennas without and with pin, respectively. The obtained 3-dB ARBWs and −10-dB IBWs make the proposed antennas entirely cover the LTE 42 or LTE 42/43 frequency bands.