An experimental and computational study of coupling between lithographically fabricated, near-single-domain nanomagnets is presented. Pairs of coupled nanomagnets were fabricated, and their switching properties were characterized by a vibrating sample magnetometer with vector coils. Coupling fields between on-chip nanomagnets compete with (known) magnetic fields that are externally generated. Consequently, nanomagnets flip in the direction of the stronger contribution. Using this method, the volume-averaged coupling field can be directly measured. The experimental data was compared to results from micromagnetic simulations and macrospin models. Correlating the experimental results with simulations reveals the details of the switching process of nanomagnets, and shows the limitations of the macrospin model.