We present detailed simulations of the Warm-Hot Intergalactic Medium (WHIM) with the gratings of Constellation-X. Simulations are based on the extrapolation of the expected number density of OVII WHIM systems from hydrodynamical simulations of the local Universe, up to redshift of z=1 and down to an OVII column density of 1014 cm-2, and assume random metallicity and internal turbulence velocities between 0.05-0.3 Solar and 0-150 km s-1 respectively. We simulated 100 ks Constelation-X/gratings exposures using a relatively bright (0.5-2 keV flux of 0.1 mCrab) quasar at z=1 as background X-ray source. About 30 of such sigtlines are available in the RASS. We show that about 20-30 percent of the expected OVII-WHIM systems will be detected in OVII K-alpha along one of these lines of sight with a grating resolving power of R=300, while this fraction rises to about unity with a resolving power of R > 3000 (sufficient to resolve the O lines in gas with a temperature of about 1e6 K). A resolving power of R=3000 will also allow us to detect the associated OVIII Ly-alpha lines and so to estimate a metallicity-independent ionization correction for most of the systems. We also explored a grating configuration that covered up to 60 A in wavelength, so to include the CV K-alpha spectral region, and estimated that C/N, C/O and O/N relative metallicity studies can be performed on about half of the expected systems with a resolving power of R=3000, but only for about 1-5 percent of the systems at a 10 times lower resolving power.