A resonant via-type connection between layers of a multilayer support structure having, at predetermined RF frequencies, a very low, effectively short circuit impedance. The resonant vias utilize the inductance of a via post by forming it into a resonant circuit with a capacitance at the via's distal end coupled to another conductor. A plurality of resonant vias can be formed having respective plurality of resonant frequencies to form a wideband connection. The capacitances at the vias' distal ends coupling to another conductor can be formed to resonate with the total series inductance of the via post and of wire connections to an attached device.