RX J1856.5-3754 and RX J0720.4-3125 are the only young isolated radio-quiet neutron stars ( NSs ) for which trigonometric parallaxes were measured . Due to detection of their thermal emission in X-rays they are important to study NS cooling and to probe theoretical cooling models . Hence , a precise determination of their age is essential . Recently , new parallax measurements of RX J1856.5-3754 and RX J0720.4-3125 were obtained . Considering that NSs may originate from binary systems that got disrupted due to an asymmetric supernova , we attempt to identify runaway stars which may have been former companions to the NS progenitors . Such an identification would strongly support a particular birth scenario with time and place . We trace back each NS , runaway star and the centres of possible birth associations ( assuming that most NSs are ejected directly from their parent association ) to find close encounters . The kinematic age is then given by the time since the encounter . We use Monte Carlo simulations to account for observational uncertainties and evaluate the outcome statistically . Using the most recent parallax measurement of 8 { . } 16 \pm 0 { . } 80 \mathrm { mas } for RX J1856.5-3754 by , we find that it originated in the Upper Scorpius association 0 { . } 46 \pm 0 { . } 05 \mathrm { Myr } ago . This kinematic age is slightly larger than the value we reported earlier ( 0 { . } 3 \mathrm { Myr } ) using the old parallax value of 5 { . } 6 \pm 0 { . } 6 \mathrm { mas } by . Our result is strongly supported by its current radial velocity that we predict to be 6 ^ { +19 } _ { -20 } \mathrm { km / s } . This implies an inclination angle to the line-of sight of 88 \pm 6 \mathrm { deg } consistent with estimates by from the bow shock . No suitable runaway star was found to be a potential former companion of RX J1856.5-3754 . Making use of a recent parallax measurement for RX J0720.4-3125 of 3 { . } 6 \pm 1 { . } 6 \mathrm { mas } by , we find that this NS was possibly born in Trumpler 10 0 { . } 85 \pm 0 { . } 15 \mathrm { Myr } ago . This kinematic age is somewhat larger than the one obtained using the old parallax value of 2 { . } 77 \pm 1 { . } 29 \mathrm { mas } by ( 0 { . } 5 \mathrm { Myr } ) . We suggest the B0 runaway supergiant HIP 43158 as a candidate for a former companion of the progenitor star . Then , the current distance of RX J0720.4-3125 to the Sun should be 286 ^ { +27 } _ { -23 } \mathrm { pc } , in agreement with recent measurements . We then expect the radial velocity of RX J0720.4-3125 to be -76 ^ { +34 } _ { -17 } \mathrm { km / s } .