We conjecture a formula for the Schur index of N=2 four-dimensional theories
in the presence of boundary conditions and/or line defects, in terms of the
low-energy effective Seiberg-Witten description of the system together with
massive BPS excitations. We test our proposal in a variety of examples for
SU(2) gauge theories, either conformal or asymptotically free. We use the
conjecture to compute these defect-enriched Schur indices for theories which
lack a Lagrangian description, such as Argyres-Douglas theories. We demonstrate
in various examples that line defect indices can be expressed as sums of
characters of the associated two-dimensional chiral algebra and that for
Argyres-Douglas theories the line defect OPE reduces in the index to the
Verlinde algebra.