  We introduce and study quantum Capelli operators inside newly constructed
quantum Weyl algebras associated to three families of symmetric pairs. Both the
center of a particular quantized enveloping algebra and the Capelli operators
act semisimply on the polynomial part of these quantum Weyl algebras. We show
how to transfer well-known properties of the center arising from the theory of
quantum symmetric pairs to the Capelli operators. Using this information, we
provide a natural realization of Knop-Sahi interpolation polynomials as
functions that produce eigenvalues for quantum Capelli operators.
