Before the US Civil War, the 11 southern states surely had representatives in Washington. Did they continue to serve in Congress through the war? Did they move to the Confederate congress in Virginia? Were they counted absent votes in the US Congress?
Several representatives from Virginia, Tennessee, and Louisiana (all repudiating secession) remained in the US Congress, and pro-secession congressmen and senators from Kentucky and Missouri were expelled and the positions re-appointed. The Louisiana and some Tennessee seats would become vacant again after the 1862 elections, and the remaining Virginia seats in the House would be re-appointed to West Virginia when that state was admitted in 1861.
The Confederate Congress was appointed through new elections; some members served in both, but there definitely wasn't a 1:1 correlation.