Many law firms working in the maritime field work on contingency, especially when the matter concerns personal injury liability. They may charge up to one-third to 40% of your judgment or settlement, but you don't have to pay anything if they lose your case.
Dont assume that your maritime case is open and shut, even if the evidence seems clear. You'll still need an experienced, reputable, and capable lawyer to argue your case in the court or to negotiate a settlement. Even if the contingency fee is high, it's generally worth the cost.