The low-energy electronic excitations in graphene are described by massless Dirac fermions that have a linear dispersion relation. Taking advantage of this ‘optics-like’ electron dynamics, generic optical elements like lenses and wave guides have been proposed for electrons in graphene. Tuning of these elements relies on the ability to adjust the carrier concentration in defined areas. However, the combination of ballistic transport and complex gating remains challenging. Here we report on the fabrication and characterization of suspended graphene p–n junctions. By local gating, resonant cavities can be defined, leading to complex Fabry–Pérot interferences. The observed conductance oscillations account for quantum interference of electrons propagating ballistically over distances exceeding 1 μm. Visibility of the interferences is demonstrated to be enhanced by Klein collimation at the p–n interface. This finding paves the way to more complex gate-controlled ballistic graphene devices and brings electron optics in graphene closer to reality.