The exoplanetary science through direct imaging and spectroscopy will largely expand with the forthcoming development of new instruments at the Very Large Telescope (VLT; SPHERE), Gemini (GPI), Subaru (HiCIAO) and Palomar (Project 1640) observatories. All these ground-based adaptive optics instruments combine extremely high performance adaptive optics systems correcting for the atmospheric turbulence with advanced starlight-cancellation techniques such as coronagraphy to deliver contrast ratios of about 10^-6 to 10^-7. While the past 15 yr have seen intensive research and the development of high-contrast coronagraph concepts, very few concepts have been tested under dynamical seeing conditions (either during sky observation or in a realistic laboratory environment). In this paper, we discuss the results obtained with four different coronagraphs - phase and amplitude types - on the High-Order Testbench, the adaptive optics facility developed at ESO. This facility emphasizes realistic conditions encountered at a telescope (e.g. VLT), including a turbulence generator and a high-order adaptive optics system. It enables to evaluate the performance of high-contrast coronagraphs in the near-infrared operating with an adaptive optics corrected point spread function of 90 per cent Strehl ratio under 0.5 arcsec dynamical seeing.