We describe a new design of a gradiometric flip-chip antenna, which is inductively coupled to a dc-SQUID gradiometer. Both components are patterned out of thin films of the high-Tc superconductor YBa2Cu3O7−x (YBCO). For the flip-chip antenna, a 40 mm × 10 mm SrTiO3 single crystalline substrate is used, while the gradiometer sensors are prepared on 10 mm × 10 mm SrTiO3 bicrystal substrates. Special attention is paid to the inductive coupling between the flip-chip antenna and the read-out gradiometer antenna. We investigate different designs of coupling loops in order to optimize the coupling inductance between both components of the sensor. With optimized coupling the sensor achieves a field-gradient resolution of 12 fT cm−1 Hz−1/2 in the white noise region and of 310 fT cm−1 Hz−1/2 at 1 Hz in the unshielded laboratory environment.