The eccentricity of the planet’s orbit and the inclination of the orbital plane carry important information about its formation and history. However, exoplanets detected via direct-imaging are often only observed for a very small fraction of their period, making it challenging to reliably estimate their orbits. The aim of this project is to investigate biases in the estimation of orbital parameters of directly-imaged exoplanets, particularly their eccentricities, and to define general guidelines to perform better estimations. For this, we constructed various orbits, and generated mock data for each spanning around 0.5% of their orbital period. We the Orbits For The Impatient (OFTI) algorithms to get orbit posteriors, and compared those to the true orbital parameters. We found that the inclination of the orbital plane is the parameter that most affects our estimations of eccentricity, with orbits that appear near-edge-on producing highly biased eccentricity posteriors. We also found a degeneracy between eccentricity and inclination that makes it ifficult to distinguish circular, edge-on orbits from eccentric, face-on orbits. For the exoplanet-imaging community, we propose practical recommendations, guidelines and warnings relevant to orbit-fitting.