Mid-IR emission lines of H2 are useful probes to determine the mass of warm gas present in the surface layers of disks. Numerous observations of Herbig Ae/Be stars (HAeBes) have been performed, but only 2 detections of mid-IR H2 toward HD97048 and AB Aur have been reported. We aim at tracing the warm gas in the disks of 5 HAeBes with gas-rich environments and physical characteristics close to those of AB Aur and HD97048, to discuss whether the detections toward these 2 objects are suggestive of peculiar conditions for the gas. We search for the H2 S(1) emission line at 17.035 mum with VISIR, and complemented by CH molecule observations with UVES. We gather the H2 measurements from the literature to put the new results in context and search for a correlation with some disk properties. None of the 5 VISIR targets shows evidence for H2 emission. From the 3sigma upper limits on the integrated line fluxes we constrain the amount of optically thin warm gas to be less than 1.4 M_Jup in the disk surface layers. There are now 20 HAeBes observed with VISIR and TEXES instruments to search for warm H2, but only two detections (HD97048 and AB Aur) were made so far. We find that the two stars with detected warm H2 show at the same time high 30/13 mum flux ratios and large PAH line fluxes at 8.6 and 11.3 mum compared to the bulk of observed HAeBes and have emission CO lines detected at 4.7 mum. We detect the CH 4300.3A absorption line toward both HD97048 and AB Aur with UVES. The CH to H2 abundance ratios that this would imply if it were to arise from the same component as well as the radial velocity of the CH lines both suggest that CH arises from a surrounding envelope, while the detected H2 would reside in the disk. The two detections of the S(1) line in the disks of HD97048 and AB Aur suggest either peculiar physical conditions or a particular stage of evolution.
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