Not necessarily. A non-dissipative resistance definition is covered in The IEEE Dictionary under "(B) the real part of impedance", i.e. no dissipation required. An example is the Z0 of a transmission line which is mostly resistive yet non-dissipative. The conjugate matching theorem applies only to lossless systems and therefore an ideal conjugate match cannot exist in reality. But it is easy to check for a near-conjugate match in a low loss system. Adjust your antenna tuner until your transmitter sees 50 ohms, i.e. an SWR of 1:1. Disconnect the transmitter cable and put a 50 ohm non-inductive resistor across the tuner input. Disconnect the tuner output and measure the impedance looking up the transmission line toward the antenna, e.g. R+jX. Measure the impedance looking back into the output terminal of the tuner. If that impedance is close to R-jX, the system is tuned to as close to a conjugate match as is possible in a real-world system with losses. In the real world, we are usually forced to settle for a Z0-match which, in a lossless system, would guarantee a conjugate match. You see, one of the premises of the conjugate matching theorem is that if there is a conjugate match at one point, there is a conjugate match at all points. Unfortunately, that can only happen in a lossless system. But if in a low-loss system we can prove that the impedance measured in one direction is nearly the conjugate of the impedance measured in the other direction, we are as close to a conjugate match as we are going to get in the real world.