  Over a closed manifold, we consider the sectorial projection of an elliptic
pseudo-differential operator A of positive order with two rays of minimal
growth. We show that it depends continuously on A when the space of
pseudo-differential operators is equipped with a certain topology which we
explicitly describe. Our main application deals with a continuous curve of
arbitrary first order linear elliptic differential operators over a compact
manifold with boundary. Under the additional assumption of the weak inner
unique continuation property, we derive the continuity of a related curve of
Calderon projections and hence of the Cauchy data spaces of the original
operator curve.
  In the Appendix, we describe a topological obstruction against a verbatim use
of R. Seeley's original argument for the complex powers, which was seemingly
overlooked in previous studies of the sectorial projection.
