Mirror Symmetry predicts a correspondence between the complex geometry (the B-side) and the symplectic geometry (the A-side) of suitable pairs of objects. In this talk I will consider certain orbifold del Pezzo surfaces falling outside of the standard mirror symmetry constructions. I will describe the derived category of coherent sheaves of the surfaces (their B-side), and discuss early results on the A-side. This is joint work with Franco Rota.