Hi Alan
I was able to find my great grandparent's marriage records at the Grodno Archive in Belarus. They were married in Lida, Belarus.
Some information was on the Jewishgen site and then, with the help of a Russian friend, I contacted the archivist at Grodno who sent me documents (all in Russian).
Ukraine I don't know about - I am searching information about my other great grandfather Moses Cohen from Wladimeretz, Wohelin, Russia (now Ukraine) - so I will follow what other replies you get with interest

good luck

Nicholas Boyarsky