  We study coisotropic submanifolds of $b$-symplectic manifolds. We prove that
$b$-coisotropic submanifolds (those transverse to the degeneracy locus)
determine the $b$-symplectic structure in a neighborhood, and provide a normal
form theorem. This extends Gotay's theorem in symplectic geometry. Further, we
introduce strong $b$-coisotropic submanifolds and show that their coisotropic
quotient, which locally is always smooth, inherits a reduced $b$-symplectic
structure.
