This study analyzes the thermodynamic, economic, and regulatory aspects of boil-off hydrogen (BOH) in liquid hydrogen (LH₂) carriers that can be re-liquefied using a proposed re-liquefaction system or used as fuel in a fuel cell stack. Five LH₂ carriers sailing between two designated ports are considered in a case study. The specific energy consumption of the proposed re-liquefaction system varies from 8.22 to 10.80 kWh/kg as the re-liquefaction-to-generation fraction (R/G fraction) is varied. The economic evaluation results show that the cost of re-liquefaction decreases as the re-liquefied flow rate increases and converges to 1.5 $/kg at an adequately large flow rate. Three energy efficient design index (EEDI) candidates are proposed to determine feasible R/G fractions: an EEDI equivalent to that of LNG carriers, an EEDI that considers the energy density of LH₂, and no EEDI restrictions. The first EEDI candidate is so strict that the majority of the BOH should be used as fuel. In the case of the second EEDI candidate, the permittable R/G fraction is between 25% and 33%. If the EEDI is not applied for LH₂ carriers, as in the third candidate, the specific life-cycle cost decreases to 67% compared with the first EEDI regulation.