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Energetic pulsars power winds of relativistic leptons which produce photon nebulae (so- called pulsar wind nebulae, PWNe). Their spectral energy distribution has a double-humped structure: the first hump lies in the X-ray regime, the second in the gamma-ray range. The X-ray emission is generally understood as synchrotron radiation by highly energetic leptons, the gamma-ray emission as Inverse Compton scattering of energetic leptons with ambient photon fields. The spectral evolution is influenced by the time-dependent spin-down of the pulsar and the decrease of the magnetic field strength with time. Thus, the present spectral appearance of a PWN depends on the age of the pulsar: while young PWNe are bright in X-rays and gamma-rays, the X-ray emission of evolved PWNe is suppressed. Hence, evolved pulsar wind nebulae may offer an explanation of the nature of some of the unidentified VHE (very high-energy, E > 100GeV) gamma-ray sources not yet associated with a counterpart at other wavelengths. The purpose of this work is to develop a model which allows to calculate the expected X-ray fluxes of unidentified VHE gamma-ray sources considered to be PWN candidates. Such an estimate may help to evaluate the prospects of detecting the X-ray signal in deep observations with current X-ray observatories in future studies. We present a time-dependent leptonic model which predicts the broad-band emission of a PWN according to the characteristics of its pulsar. For a sample of representative PWNe, the resulting model predictions in the X-ray and gamma-ray range are compared to observations. The comparison shows that the energy flux of the X-ray emission of identified PWNe from different states of evolution can be roughly predicted by the model. This implies the possibility of an estimate of the non-thermal X-ray emission of unidentified VHE gamma-ray sources in case of an evolved PWN scenario.