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It is well known that high contrast substrates, although suitable for miniaturization lead to smaller bandwidth. To overcome this limitation, a combined shape and material optimization technique is proposed to develop a miniature patch antenna with pre-specified bandwidth performance. The employed design method is the solid isotropic material with penalization (SIMP) technique formulated as a general non-linear optimization problem. As part of the solution technique an adjoint sensitivity analysis and the sequential linear programming method (SLP) are adapted. A key aspect of the proposed design method is the integration of optimization tools with a fast simulator based on the finite element-boundary integral method. This allowed for inhomogeneous material modeling and design to increase the bandwidth of a fixed size patch antenna on a high contrast substrate having a dielectric constant of εr=100.