My daughter and son-in-law emigrated to New Zealand (Wellington) nearly 7 years ago and our grandson was born two years later - he will be 5 in February. There is a lot of wisdom in so much that has been written since Frances posted her first message. The things that are most important in my experience are:
1) Keep in touch by every possible means, camera Skype, text Skype, email, Facebook, cards and notes, small presents, anything (but keep it as fun as possible); and don't worry if the return is less - they are much busier than we are!
2) If you can manage visits, that is great. We have been very lucky in being retired and able to downsize to afford trips - we have also found that staying in a nearby apartment is a better solution than staying with them - easier for everyone.
3) Don't be afraid to acknowledge that you miss each other - never mind us, our little grandson is very very sad when we leave and it's important to talk about this with them and not to brush it under the carpet.
4) Homesickness on their part is normal. It does not mean they should come back! - and the quality of life they went there to find is usually much better than they could get if they came back here.
It has given us a whole new dimension to our lives - and actually, migration is a normal human activity (that's how our ancestors got to Britain!) - we are so lucky in this day and age to have the technology to communicate and visit relatively easily.
Good luck to all long-distance grans!