Passive intermodulation (PIM) by metal contacts limits the bandwidth and capacity of radio links used in mobile and satellite communications. In this work, we investigate the effect of nonlinearities in metal-insulator-metal (MIM) contacts and their effects on PIM generation. An analytical expression is obtained for the tunneling current density which has an error of ~1.6% in the case of a very thin insulator and low voltages in MIM junctions. The presented analytical model of the contact surfaces with the fractal geometry is used to simulate PIM products of third-order (PIM3) and fifth-order (PIM5) versus the contact resistance and applied pressure. The simulation results are validated experimentally by an open-ended rectangular coaxial structure with a slotted enclosure. The measurement results demonstrate that the presented model predicts the PIM with a mean error of about 4.8 dB when the contact pressure varies from 0.5 to 1.7 MPa.