  We classify symplectic 4-dimensional semifields over $\mathbb{F}_q$, for
$q\leq 9$, thereby extending (and confirming) the previously obtained
classifications for $q\leq 7$. The classification is obtained by classifying
all symplectic semifield subspaces in $\mathrm{PG}(9,q)$ for $q\leq 9$ up to
$K$-equivalence, where $K\leq \mathrm{PGL}(10,q)$ is the lift of
$\mathrm{PGL}(4,q)$ under the Veronese embedding of $\mathrm{PG}(3,q)$ in
$\mathrm{PG}(9,q)$ of degree two. Our results imply the non-existence of
non-associative symplectic 4-dimensional semifields for $q$ even, $q\leq 8$.
For $q$ odd, and $q\leq 9$, our results imply that the isotopism class of a
symplectic non-associative 4-dimensional semifield over $\mathbb{F}_q$ is
contained in the Knuth orbit of a Dickson commutative semifield.
