We report a complete procedure to achieve multilayer YBa2Cu3O7-δ (YBCO) thick films by electrophoretic deposition on silver tubes using a suspension of YBCO powder in butanol. With the aim to optimize the magnetic shielding performances of the coatings, we have carried out an extensive investigation of the influence of the deposition parameters, the multilayer deposition sequence and the intermediate/final heat treatments on the coating microsfructure. Using the optimized conditions, a 24-layer YBCO coating has been successfully prepared on an 80 mm long Ag tube: the melt growth processed multilayered YBCO thick film thus obtained can shield an applied magnetic field of 1.9 mT at 77 K, the highest value per thickness unit reported so far in the literature for these materials.