Simultaneous X-ray and UV observations of the Seyfert 1 galaxy NGC 3516 were carried out to investigate the connection between the variable X-ray and ultraviolet absorption features. Over a 2 week period, X-ray spectra were obtained with Ginga, simultaneously with UV spectra from IUE. The X-ray spectrum was complex and could be fitted satisfactorily with a warm absorber model, a partial covering model, or a cold reflector model, in addition to an overlying column density of N(H) is similar to 4 x 10(22) cm-2. The X-ray absorption remained unchanged (in all the spectral models), while the spectral index alpha changed significantly. The Fe Kalpha line was generally found to be strong (EW is similar to 250-400 eV). The UV spectra displayed a significant variation in the continuum flux, while the absorption features in the C IV lambda1550, N V lambda1240, and Si IV lambda1400 lines stayed constant. A common origin of the UV and X-ray absorption could not be established due to the absence of variability in either the X-ray or the UV absorption. A lower limit on the column densities of the UV absorber is approximately 2 x 10(19) cm-2. Assuming that the variability in the C IV lambda1550 absorption (as detected in the archival data) is due to changes in the ionization level, the UV absorbers should be located closer than 9 pc from the ionizing source for log N(H) is similar to 20, and at smaller distances for higher column densities. Based on estimates of the absorbing properties of a low-luminosity AGN in the framework of broad absorption line (BAL) theories, we suggest that NGC 3516 is consistent with a low-luminosity equivalent of a BAL QSO. Finally, we discuss the likely location of the UV absorbers in optically thin clouds in the broad line region. A common origin of the UV and X-ray absorption in such clouds is probably ruled out.