A design methodology is presented for the optimization of conformal antennas with Electromagnetic Bandgap (EBG) surfaces to improve antenna performance. The EBG surface is obtained by utilizing a Frequency Selective Surface (FSS) on top of a thin dielectric substrate backed by a metallic ground plane, to act as an Artificial Magnetic Conductor (AMC). The antenna is then placed above the EBG surface to create the integrated EBG conformal antenna. This research demonstrates the ability to optimize both the antenna and EBG surface simultaneously in order to achieve improved antenna performance compared to the antenna and the EBG surface optimized separately. Results are presented for a broadband EBG conformal antenna system that operates from 5.5 to 7.1 GHz with a center frequency of 6.3 GHz.