Using solid-state nanopores with optical tweezers, we perform force spectroscopy on DNA molecules that are coated with RecA proteins. We observe that the electrophoretic force is 2-4 times larger for RecA-DNA filaments than for uncoated DNA molecules and that this force increases at lower salt concentrations. The data demonstrate the efficacy of solid-state nanopores for locally probing the forces on DNA-bound proteins. Our results are described quantitatively by a model that treats the electrophoretic and hydrodynamic forces. The conductance steps that occur when RecA-DNA enters the nanopore change from conductance decreases at high salt to conductance increases at low salt, which allows the apparent charge of the RecA-DNA filament to be extracted. The combination of conductance measurements with local force spectroscopy increases the potential for future solid-state nanopore screening devices.