I want to know if there is a uniqueness (in any sense) theorem for the symplectic structure in a neighborhood of a symplectic surface in a four dimensional symplectic manifold. Or more generally for any configuartion of symplectic surfaces. 



neighborhood of symplectic surfaces
Here is the version of the Darboux-Weinstein theorem that you want to use: Let $(M\_1,\omega\_1)$ and $(M\_2,\omega\_2)$ be symplectic manifolds of dimension $2n$ and let $\iota\_i:P\to M\_i$ be smooth embeddings with the property that there exists an isomorphism $\phi:\iota\_1^\*(TM\_1)\to \iota\_2^\*(TM\_2)$ of vector bundles such that $\phi^\*(\omega\_2) = \omega\_1$ (i.e., $\phi$ is a symplectic isomorphism) and, moreover, $\phi(\iota\_1'(v)) = \iota\_2'(v)$ for all $v\in TP$. Then there exist open neighborhoods $U\_i\subset M\_i$ of $\iota\_i(P)$ and a symplectomorphism $\Phi:(U\_1,\omega\_1)\to(U\_2,\omega\_2)$ such that $\Phi\circ\iota\_1 = \iota\_2$.


Thus, the symplectic structure near an embedded symplectic surface $P$ in a symplectic $4$-manifold $(M,\omega)$ is determined by the isomorphism class of its (oriented) normal bundle (plus, of course, the symplectic area of $P$, i.e., the integral of $\omega$ over $P$).


