We report on our recent efforts to compute the X-ray emission from the hot, shocked stellar wind gas filling the inner cavity of planetary nebulae. To this end, we updated our 1D hydrodynamics code NEBEL by including a module that computes the heat transfer by thermal conduction across the contact discontinuity separating the hot shocked wind gas from the much cooler nebular material. Given the temperature and density structure of the hot bubble the X-ray emission is computed by means of the CHIANTI code. We find a reasonably close agreement of the computed X-ray luminosities with recent observations of Newton-XMM and Chandra. Our simulations also predict how the X-ray emission depends on the wind luminosity and the stellar parameters.