  In four-dimensional N=2 compactifications of string theory or M-theory,
modifications of the Bekenstein-Hawking area law for black hole entropy in the
presence of higher-derivative interactions are crucial for finding agreement
between the macroscopic entropy obtained from supergravity and subleading
corrections to the microscopic entropy obtained via state counting. Here we
compute the modifications to the area law for various classes of black holes,
such as heterotic black holes, stemming from certain higher-derivative
gravitational Wilsonian coupling functions. We consider the extension to
heterotic N=4 supersymmetric black holes and their type-II duals and we discuss
its implications for the corresponding micro-state counting. In the effective
field theory approach the Wilsonian coupling functions are known to receive
non-holomorphic corrections. We discuss how to incorporate such corrections
into macroscopic entropy formulae so as to render them invariant under duality
transformations, and we give a concrete example thereof.
