There are two ways of looking at refugees (and consequently at this particular topic of discussion). Either they are a separate people who are kept in a separate (from the rest of the host countries society) place of waiting until their country has stabilized before being returned; or they are people who must be forced immigrants who wish to become a part of the countries they flee to.
In the first scenario the case can be strongly made for the host country to recognize as many of the refugees cultural norms of the refugees as possible, without infringing on the rights on the host country's people. Therefore, for the particular case of child marriages, you would allow these marriages to continue but you would not allow a refugee to marry an underage citizen on the host country and you would not issue marriage licences to refugees if one of the participants is underage.
In the second scenario, where you are assuming that the refugees are in fact immigrants who want to integrate into the host society, then a case can be made for the host country to be much less compromising with the refugees.
I believe there is a compromise that can be struck between these two positions. Refugees can be placed in separate camps where they may continue, largely untroubled with most of their cultural arrangements within limits. Or they may choose to opt into their host country and in doing so commit to living and upholding the laws and ordinances of the host country and do all they have to do to make themselves compliant (including divorce if necessary).