The treatment of kinetic shear Alfven waves in homogeneous magnetized plasmas by means of Vlasov simulation is examined. To this end, the driftkinetic version of the Vlasov-Maxwell equations is solved via various numerical schemes, all employing a grid in (1 + 1)D phase space. Since kinetic shear Alfven waves are Landau damped, the use of an equidistant grid in velocity space leads to a recurrence problem. The latter can be circumvented, however, by damping the finest velocity space scales through higher-order collision operators. Of particular interest is the question if and under which circumstances the magnetohydrodynamic limit (small perpendicular wavenumber) can be recovered.