A new experimental technique is proposed to easily measure both advancing and receding contact angles of a liquid on a solid surface, with unprecedented accuracy. The technique is based on the analysis of the evolution of a capillary bridge formed between a liquid bath and a solid surface (which needs to be spherical) when the distance between the surface and the liquid bath is slowly varied. The feasibility of the technique is demonstrated using a low-energy perfluorinated surface with two different test liquids (water and hexadecane). A detailed description of both experimental procedures and computational modeling are given, allowing one to determine contact angle values. It is shown that the origin of the high accuracy of this technique relies on the fact that the contact angles are automatically averaged over the whole periphery of the contact. This method appears to be particularly adapted to the characterization of surfaces with very low contact angle hysteresis.