We report the design, fabrication and outdoor characterization of a tandem luminescent solar concentrator/Si multi-junction photovoltaic module. Our tandem LSC/Si device consists of an InGaP LSC functioning as a top cell and a passivated contact Si bottom cell. The LSC comprises of an InGaP microcell array coupled to a polymer waveguide, loaded with CdSe/CdS core-shell quantum dot luminophores. The light trapping efficiency of the LSC waveguide is enhanced by encapsulation with photoluminescence trapping mirrors consisting of dielectric multilayer thin films. We demonstrate the performance of the LSC/Si device through a series of outdoor tests under various irradiance conditions conducted at the National Renewable Energy Laboratory. We report the first outdoor testing data of an LSC/Si tandem module, displaying maintained performance across varied diffusivity conditions for the LSC component. Finally, we model the tandem module performance using a ray optic simulation-based multiphysics model and forecast a pathway for high efficiency tandem LSC/Si module performance.