  We construct a natural semiorthogonal decomposition for the derived category
of an arbitrary flat family of sextic del Pezzo surfaces with at worst du Val
singularities. This decomposition has three components equivalent to twisted
derived categories of finite flat schemes of degrees 1, 3, and 2 over the base
of the family. We provide a modular interpretation for these schemes and
compute them explicitly in a number of standard families. For two such families
the computation is based on a symmetric version of homological projective
duality for $\mathbb{P}^2 \times \mathbb{P}^2$ and $\mathbb{P}^1 \times
\mathbb{P}^1 \times \mathbb{P}^1$, which we explain in an appendix.
