Just hot of the heels of completing ME2 and I'm pretty sweeped by how amazing it was. Overall I was pretty happy with the save I've got for ME3 but I failed to get the romance with Miranda I was after; which cheeses me off the more I think about it. I completed it in 24 hours and I guess I'm willing to jump back to a save from 19 or more hours -- but can't really be arsed about going back further (mainly because recruitment and loyalty missions take 45 minutes each..) to get the romance.  
 
I don't know why I didn't get it though, I did all the loyalty missions and headed down to see Miranda after every mission, as well as help her in her bitchy argument with Jack. But all I get when I ask to talk to her is "I'm a bit busy at the moment...". I never got another chance to have a discussion with her for about half the game or something. Does anyone know what I've done wrong?

That happend to me too, ended up with the quarian 
I think i will do another playthrough and not take jacks side

She should have opened up after her loyalty mission. If not you probably said something wrong earlier.

Man Romance is a thing in this game,  I brought Miranda up to her basically offering a relationship and said I wasn't interested since i'm going for Tali this playthrough, but now things are really weird between me and Jack because I think I missed denying a relationship and now I can't let her down without making her hate me.

Miranda was mad interested in my Shepard, but hey... Tali. Shepard and Tali had a nice connection in the first game, and it just developed further this time. 
I did most, if not all, of the talking the paragon way. So I didn't side with anyone when Jack and Miranda fought, but made them calm down instead. Maybe that is where you went wrong? Kinda hard to say. A lot of choices throughout the game that can affect things.

I had no problem dicking down Miranda in my first play through. Hell, I even bedded Jack early on in the game. All I did was consider her opinions when I made choices.

I didn't have problems with Miranda, and wasn't even trying. I think a lot of it has to do with conversation choices early on. I don't think it takes much to derail the situation given how many conversation options there are with so many characters. On another playthrough (staying loyal to Liara from ME1) I found that things were progressing with Jack more than I liked (again, not even trying). I wish there was a better way of keeping track of where you stood with some characters when it comes to romance. I think the game developers saw some conversation choices as advancing the romance when it's not universally clear that's what the reasonable result would be.

The girls I've romanced as Male Sheperd are Tali, and Jack on seperate playthroughs.

On my latest playthrough, I romanced Jacob.

Next up, Miranda.  But that will be someday.

How can you miss one of these? I accidentally got Miranda and Jack just by taking the top right dialogue option. 
 
You probably don't get it if you don't make the speech check on Jack and Miranda's confrontation and side with Jack, since that makes her lose loyalty.