  In this paper we establish two boundary versions of the Schwarz lemma. The
first is for general holomorphic self maps of bounded convex domains with $C^2$
boundary. This appears to be the first boundary Schwarz lemma for general
holomorphic self maps that requires no strong pseudoconvexity or finite type
assumptions. The second is for biholomorphisms of domains who have an invariant
K\"ahler metric with bounded sectional curvature. This second result applies to
holomorphic homogeneous regular domains and appears to be the first boundary
Schwarz lemma that makes no assumptions on the regularity of the boundary.
