We describe a new setup for simultaneous measurements of force and current in conductive nanocontacts in a liquid environment with a high sampling rate and resolution. A lab-built current-to-voltage converter allows measurements of the current over seven orders of magnitude. As examples, we studied conductances and mechanical forces upon formation and breaking of gold atomic contacts and of two molecular junctions containing 1,2-di(4-pyridyl)ethyne (M1) and 1,4-di(4-pyridyl)buta-1,3-diyne (M2). We found that the forces required to deform or break gold atomic contacts depend critically on the surrounding medium. Further, they show non-linear behaviour in dependence of the number N of gold atoms detached. The electromechanical properties of the two types of molecular junctions upon stretching were analysed by correlating breaking forces with simultaneously measured junction conductances. A rather complex behaviour in a wide range of forces was discovered. Comparison of the current-probe atomic force microscopy experiments on the rupture of molecular junctions with STM-based break junction experiments enables the assignment of breaking forces of molecular junctions to the corresponding junction conductances.