Maximally entangled numerical shadow of a matrix $A$ of size $d=d_1\times d_2$ is defined as a probability distribution $P_A(z)$ on the complex plane, supported on the maximally entangled numerical range $W^\mathrm{ent}(A)$. $$ P_A(z) := \int_{\Omega} {\rm d} \mu(\psi) \delta\Bigl( z-\langle \psi|A|\psi\rangle\Bigr), $$ where $\mu(\psi)$ denotes the unique unitarily invariant (Fubini-Study) measure on the set $$ \Omega=\{\ket{\psi} \in \mathbb{C}^{d_1\times d_2}: \ket{\psi}=\frac{1}{\sqrt{d_\min}} (U_1\otimes U_2)\sum_{i=1}^{d_\min} \ket{\psi_i^1}\otimes \ket{\psi_i^2} \}, $$ where