A catheter arrangement includes a flexible shaft having a length sufficient to access a patient's renal artery relative to a percutaneous access location. A cooling arrangement is provided at a distal end of the shaft and dimensioned for deployment within a renal artery. The cooling arrangement is configured to freeze tissue of a wall of the renal artery while target tissue adjacent the renal artery wall including perivascular renal nerve tissue remains unfrozen. A microwave emitter is configured to propagate microwave energy through the frozen renal artery wall to heat the unfrozen target tissue to a temperature sufficient to ablate perivascular renal nerve tissue included within the target tissue with no or negligible thermal damage to at least an inner wall of the renal artery.