An electronic device may include a transmission line path having a signal conductor embedded in a substrate. A contact pad may be patterned on a surface of the substrate. A radio-frequency component may be mounted to the contact pad using solder. Multi-layer impedance matching structures may couple the signal conductor to the contact pad. The matching structures may include a set of via pads and a set of conductive vias coupled in series between the signal conductor and the contact pad. The area of the via pads may vary across the set of via pads and/or the aspect ratio of the conductive vias may vary across the set of conductive vias. The matching structures may perform impedance matching between the signal conductor and the radio-frequency component at frequencies greater than 10 GHz while occupying a minimal amount of space in the device.