Vertically integrated graphene-semiconductor systems remain of significant technological importance for their promise to captivate new device physics and propel the development of advanced carbon-based opto-electronic devices. In this study, we carry out a series of bias-dependent transport, gate-dependent transport, and photoconduction measurements to probe the opto-electronic characteristics of metal-graphene-4H-SiC (0001) (Si-face) heterojunctions. The forward bias transport is found to deviate strongly from thermionic emission one as being controlled by the device circuitry and minority carrier injection mechanisms. An improved analytical model is offered and used to extract key junction parameters including series resistance of ∼80 kΩ, interface barrier height of ∼0.6 eV, and ideality factor of ∼6.1. The results of the photocurrent tests point to a light-assisted minority carrier injection as a key mechanism behind the photoconductive gain obtained in the devices subject to a weak, sub-bandgap cw-excitation.