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 and reduce leakage, a novel stepped shaft PDS is hereby introduced. The invention has a unique arrangement of steps on the rotor surface, each facing an upstream rib in a pocket row. Thus, 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). The convergence-divergence variation of cross-section areas along the flow direction increases the PDS damping coefficient. To validate the performance of the novel design, a stepped shaft PDS (c1/c2 = 0.5) with four axial ribs and eight circumferential pockets is built and tested. A comprehensive investigation, experimental and computational, produces the seal leakage and dynamic force coefficients for the stepped shaft PDS, as well as similar performance characteristics for an identical PDS with a smooth rotor surface (c1/c2 = 1, i.e., a uniform clearance PDS). The stepped shaft PDS operates with air at supply pressure (PS) ranging from 1.1 bar to 3.2 bar. The measured leakage for the stepped shaft PDS is 50% of that for the uniform clearance PDS. Computational fluid dynamics (CFD) and bulk flow model (BFM) predictions of leakage agree well with the test data. For PS = 2.3 bar, the test damping coefficient (C) for the stepped shaft PDS is ∼ 1.5 times greater than the one for the uniform clearance PDS. With an increase in PS to 3.2 bar, the stepped shaft PDS shows a two and one half increase in damping coefficient. In comparison to the test data, a CFD model over estimates C by 29% for operation at PS = 3.2 bar, though capturing the variation trend versus whirl frequency. The BFM largely under predicts C for the stepped shaft PDS and is abandoned for future work. Both the test data and CFD predictions demonstrate the superior damping performance of the stepped shaft PDS, thus providing a novel alternative seal configuration for turbomachinery usage.