High performance turbomachinery favors annular seals with a large damping coefficient to ensure rotor system stability. Pocket damper seals (PDSs), a variation of labyrinth seals with axial blades (ribs) and adding circumferential partition walls (ridges), produce a favorable damping performance. To further enhance the damping characteristic, a novel stepped shaft PDS is hereby introduced. The invention has a unique arrangement of steps on the rotor, each facing an upstream rib in a pocket. The step and a blade tip form a tight clearance (c1), while the rotor surface and the downstream blade tip make a larger clearance (c2). To validate the invention performance, a stepped shaft PDS (c1/c2 = 0.5) with four ribs and eight pockets is built and tested. For supply pressure (Ps) = 1.1 bar to 3.2 bar, the measured leakage for the stepped shaft PDS is 50% of that for an identical PDS with a smooth rotor surface (c1/c2 = 1, i.e., a uniform clearance PDS). Computational fluid dynamics (CFD) and bulk flow model predicted leakages agree well with the measurements. For Ps = 2.3 bar, the test damping coefficient for the stepped shaft PDS is ~ 1.5 times greater than that for the uniform clearance PDS. With an increase in Ps to 3.2 bar, the stepped shaft PDS shows a 2.5 times increase in damping coefficient. Both the test data and CFD predictions demonstrate the superior damping performance of the invention, thus providing a novel alternative seal configuration for turbomachinery usage.