OK, for older records that information and those links are great. I'm not necessarily looking for Birth or Death Certificates - I'm happy with any information I can get - usually Birth/Death register entries.
But I'm still intrigued by more recent information not being easy to get hold of. I'm pretty sure I'm making a real beginners error here but how could I get any information about the death of someone after 1973?
For example, I have an uncle born 20/01/1910 in Belfast and I can't find any details of his death, which might be as recent as 2000 - his siblings all lived to a ripe old age.
How would I get any information about his death?
Recent information can be difficult to find. Check the burial sites mentioned (there are more links in ANTRIM RESOURCES), search online newspapers (check not just name but any address you have, etc.), google name not just of deceased but any family of his that you know about, check with other relatives.
Otherwise you'll probably need to either GRONI or PRONI in Belfast to search more recent deaths.
