Symbiotic stars are long-period interacting binaries where the compact object, most commonly a white dwarf, is embedded in the dense stellar wind of an evolved companion star. Ultraviolet and soft X-ray emission of the accretion disc and the nuclear-burning white dwarf plays a major role in shaping the ionization balance of the surrounding wind material, giving rise to the rich line emission. In this paper, we employ two-dimensional photoionization calculations based on the cloudy code to study the ionization state of the circumbinary material in symbiotic systems and to predict their emission-line spectra. Our simulations are parametrized via the orbital parameters of the binary and the wind mass-loss rate of the donor star, while the mass accretion rate, temperature and luminosity of the white dwarf are computed self-consistently. We explore the parameter space of symbiotic binaries and compute luminosities of various astrophysically important emission lines. The line ratios are compared with traditional diagnostic diagrams used to distinguish symbiotic binaries from other types of sources, and it is shown how the binary system parameters shape these diagrams. In the significant part of the parameter space, the wind material is nearly fully ionized, except for the ‘shadow’ behind the donor star, so the white dwarf emission is typically freely escaping the system.