The masses of the nuclides ^203-207Rn and ²¹³Ra were measured directly for the first time with the Penning-trap mass spectrometer SHIPTRAP at GSI Darmstadt. The results confirm the previously determined mass values. The mass uncertainties for ²⁰⁵Rn and ²¹³Ra were significantly reduced. The results are relevant for the investigation of the nuclear shell structure between N = 82 and N = 126. As an indicator of structural changes the two-neutron separation energies S_2n(Z,N) have been studied.