Re-bottling port?

I hope I can drop in with the following query with regard to some old port. The corks are looking pretty dodgy and a couple of bottles of the dozen have either leaked or evaporated and have had to be thrown out. Does anyone know how to go about re-bottling and re-corking some old port? I'm sure I've read/heard this can be done but have no idea where to start. And is it essential to re-bottle, or can we just re-cork, instead? Because this isn't my port but belongs to my son and has to be transported some distance, either by air or sea, I think I'd rather a specialist undertook the work. Does anyone happen to know of a company that will do this? Many thanks.