The old and metal-rich open cluster NGC 6253 was observed with the Fibre Large Array Multi Element Spectrograph (FLAMES) multi-object spectrograph during an extensive radial velocity campaign monitoring 317 stars with a median of 15 epochs per object. All the targeted stars are located along the upper main sequence of the cluster between 14.8 < V < 16.5. Fifty nine stars are confirmed cluster members both by radial velocities and proper motions and do not show evidence of variability. We detected 45 variable stars among which 25 belong to NGC 6253. We were able to derive an orbital solution for four cluster members (and for two field stars) yielding minimum masses in between -90 Mi and-460 Mi and periods between 3 and 220 d. Simulations demonstrated that this survey was sensitive to objects down to 30 Ml at 10 days orbital periods with a detection efficiency equal to 50 per cent. On the basis of these results we concluded that the observed frequency of binaries down to the hydrogen burning limit and up to 20 d orbital period is around (1.5 1.3) per cent in NGC 6253. The overall observed frequency of binaries around the sample of cluster stars is (13 3) per cent. The median radial velocity precision achieved by the GIRAFFE spectrograph in this magnitude ange was around -240 m s(-1) (-180 m s(-1) for UVES). Based on a limited follow-up analysis of seven stars in our sample with the High Accuracy Radial velocity Planet Searcher (HARPS) spectrograph we determined that a precision of 35 m s-1 can be reached in this magnitude range, offering the possibility to further extend the variability analysis into the substellar domain. Prospects are even more favourable once considering the upcoming ESPRESSO spectrograph at VLT.