The data collected with a radioactively pure ZnWO$_4$ crystal scintillator (699 g) in low background measurements during 2130 h at the underground (3600 m w.e.) Laboratori Nazionali del Gran Sasso (INFN, Italy) were used to set a limit on possible concentration of superheavy eka-W (seaborgium Sg, Z = 106) in the crystal. Assuming that one of the daughters in a chain of decays of the initial Sg nucleus decays with emission of high energy $alpha$ particle ($Q_alpha > 8$ MeV) and analyzing the high energy part of the measured $alpha$ spectrum, the limit N(Sg)/N(W) < 5.5 $times$ 10$^{-14}$ atoms/atom at 90% C.L. was obtained (for Sg half-life of 10$^9$ yr). In addition, a limit on the concentration of eka-Bi was set by analysing the data collected with a large BGO scintillation bolometer in an experiment performed by another group [L. Cardani et al., JINST 7 (2012) P10022]: N(eka-Bi)/N(Bi) < 1.1 $times$ 10$^{-13}$ atoms/atom with 90% C.L. Both the limits are comparable with those obtained in recent experiments which instead look for spontaneous fission of superheavy elements or use the accelerator mass spectrometry.
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