We have studied the feasibility of making sharp and clean electrical contacts with high temperature superconductors by cleaving single crystal Y-Ba-Cu-O and Bi-Sr-Ca-Cu-O films in the stream of evaporated noble metals forming SN contacts at the revealed cross-sectional edge surfaces of the films. With this technique, we have consistently obtained contact resistances in the order of 10(-9) to 10(-8) OMEGA-cm2. From a structure with an oxide/Au/oxide configuration, the interface resistance was found to show a flat temperature dependence below T(c). Material dependence and anisotropy were observed in the contact resistance.