1. Incompatible frequency bands used by US mobile phone and Russian mobile operators?
   GSM:

• USA uses 850 mhz and 1900 mhz
• Russia uses 900 mhz and 1800 mhz (Russia also has 450 mhz)
  At the time many US mobile phone operators were using the IS-95 standard and had phones not compatible with GSM.
  Phones at the time were mostly dual-band for the 2 major frequencies in use in the Country they were bought in. To be able to effectively use a US Phone in Russia it has to be at least tri-band if not quad-band.
  The iPhone G1 had just come out the previous year, few people would have this multi-band phone at the time.

2. If they did have compatibility, high roaming costs?

@mesique2008 Not much of a travel "affacinando" [??? you made up this word, no???], are you?
I got separated from my travel partner in a train station in Italy, and it took all of 30 seconds.
We had loaded our bags onto the train when we realized we were in a smoking car. Rather than drag our bags thru the train, I hopped onto the platform to look for a nonsmoking car, which in Europe are marked on the outside with a symbol [cigarette w/international "no" symbol stamped on top of it]
Just at that moment, the engineer decided to leave 10 minutes early since the platform was empty, and it appeared no other passengers planned to board. Since I had exited the train, I assume he thought I was getting off, not planning to re-board on a non-smoking car. The train started to roll, & I was afraid to incur an injury by trying to jump onto the steps of a moving train, so I waved to my friend who was at the window. He yelled "Don't worry, I'll be back!", and I ended up stuck in Bologna with no coat, no money, no ID, no phone, nothing. The station employees were very kind and gave me free coffee and food until my fried returned 5 hours later.
So yes, it happens, even to seasoned travelers.

I guess that cell phone services are readily available in cities along the transsiberian, although of course not in all Siberia generally.
More reasonable explanations are that they were either having uncompatible cell phones (ie. not GSM) or like many who spend time in a foreign country left their own phones at home (to avoid paying for long distance calls) and bought low-cost chinese phones with chinese service and discarded them before the journey.
And I don't see why they shouldn't get separated. Russia is, after all, fairly safe and "western", you can quite easily find at least someone who speaks english and Roy was just going to a nearby rail yard during the 20 minutes-or-something stop.

Kingley's character has a cell phone and uses it. As others have pointed out, the Americans' cell phones probably wouldn't have worked in Siberia regardless of the presence or absence of cell phone coverage.

Half of the suspense of the film comes from the fact that they are in Siberiawhich is one of the most remote places on the planet.
I guess you missed that part
Siberia is about 8 times the size of Europeand there's very little going on
Some of you will remember that I have an extraordinary visual sense

This message has been deleted.

What's the point in endlessly debating such minute details as the prevalence of cell phone coverage in Russia? So much of what make movies effective depends on whether an audience member can suspend a certain amount of belief. The "all-encompassing" point of movies is (Other than artistic purposes) to entertain, not to provide nit-picky viewers with fuel to debate over in a forum. I am sick of seeing all these ridiculous posts on here. I would rather talk about relevant subjects relating to the bigger picture of the movie. Come on!

even if they had cellphones, what indication is there that they would work. it has only been a few years since people from north america could even use their phones outside of north america (the advent of GSM phones). even then, that's in places like hong kong or the UK. not siberia.
and even if the couple did have GSM phones, what indication is there that there would be service in siberia of all places?
So for them to have cell phones that worked they would need a whole set of convenient circumstances that are probably not all going to happen.

Do Americans generally own cell phones that would work in China or Russia?
I know I don't. Heck my cell phone "barely" worked in Canada.

I wonder , when this movie is supposed to take place. If it's mid-late 90-s than there would be not as many cellphones around as there are today.

As everyone else said, there's no cell phone reception in Siberia. But I wondered why they didn't communicate via email. There would probably have been internet access in both of those villages.

Maybe they don't get separated, as a rule, but actually they did. In dramatic situations people don't behave the way they do at the mall. You see a lot of pictures with cellphones. Not this one. Sorry.
Next.
If pigs had wings the sh*t of this world would be perfectly shared

Yeah, maybe they had. Alas, would you expect a lot of coverage in Siberia?
If pigs had wings the sh*t of this world would be perfectly shared

Yes, it's stupid! I mean, it's not like the entire Siberia is a cold desolate place void of all life and any traces of technology! It really isn't! There are repeater towers EVERYWHERE, set up just for the case someone wants to call someone else from the most dead end place on Earth.