Non-thermal radiation has been predicted within bow shocks around runaway stars by recent theoretical works. We present X-ray observations toward the runaway stars ζ Oph by Chandra and Suzaku and of BD+43°3654 by XMM-Newton to search for the presence of non-thermal X-ray emission. We found no evidence of non-thermal emission spatially coincident with the bow shocks; nonetheless, diffuse emission was detected in the vicinity of ζ Oph. After a careful analysis of its spectral characteristics, we conclude that this emission has a thermal nature with a plasma temperature of T ≈ 2 × 106 K. The cometary shape of this emission seems to be in line with recent predictions of radiation-hydrodynamic models of runaway stars. The case of BD+43°3654 is puzzling, as non-thermal emission has been reported in a previous work for this source.