  The quadrupole resonator (QPR) is a dedicated sample-test cavity for the RF
characterization of superconducting samples in a wide temperature, RF field and
frequency range. Its main purpose are high resolution measurements of the
surface resistance with direct access to the residual resistance thanks to the
low frequency of the first operating quadrupole mode. Besides the well-known
high resolution of the QPR, a bias of measurement data towards higher values
has been observed, especially at higher harmonic quadrupole modes. Numerical
studies show that this can be explained by parasitic RF losses on the adapter
flange used to mount samples into the QPR. Coating several micrometer of
niobium on those surfaces of the stainless steel flange that are exposed to the
RF fields significantly reduced this bias, enabling a direct measurement of a
residual resistance smaller than 5 n$\Omega$ at 2 K and 413 MHz. A constant
correction based on simulations was not feasible due to deviations from one
measurement to another. However, this issue is resolved given these new
results.
