Hi Sarbob13
I am so sorry to hear of your losses. 
I am at the same stage as you unfortunatley (just about to miscarry number 3 in a row). Unfortunately I am not a Mum yet. I have been trying since I was aged 38 and I am now 41. First pregnancy was not a miscarriage. It was in Oct 2014 where I decided to end the pregnancy at 13.5 weeks as the baby had Down's Syndrome and was extremely ill and very unlikely to have made it. I then waited a year to try again due to the devastation. In Oct 2015 I had my first miscarry (empty sac known as a blighted ovum), then again in Jan 2016 I had my second miscarry (this time had heartbeat at 7 weeks and m/c'd at 9 wks), and now again is my 3rd miscarry - discovered at 6 weeks / 3 days just a fetal pole and yolk and baby just hasn't made it
.
I tried the NHS route and they do very basic tests (the minimum). The tests they did were to check for antiphospholipid/APPT (blood clotting) and they also carried out a pelvic scan to check the anatomy ie. uterus and ovaries look ok etc. All these tests came back normal and they just told me to keep trying so I did but now suffering with 3rd miscarry. They are now referring me to a doctor called Mr Himanshu Borase and after waiting 4 weeks I still have no appointment letter to see him yet.
Regarding the NHS initial tests, you can take a look at the NHS recurrent miscarriage website to see what they test for (www.nhs.uk/Conditions/Miscarriage/Pages/Diagnosis.aspx) you'll see it's very basic stuff. If these come back normal then it's up to each NHS hospital who they refer their patients to next.
At the point after having two miscarriages in Jan 2016, although I was under NHS care I wanted more help as the NHS are too slow and I do not have time to waste. After doing some research particularly on Mumsnet, I came accross a highly recommended private doctor called Dr Shehata (www.miscarriageclinic.co.uk/). I contacted them and made my first appointment which was late April (quite a long wait). So I am now currently under Shehata's care and waiting results of blood tests. Shehata thinks I have thyroid antibodies that are attacking my pregnancies (as I was diagnosed with an overactive thyroid in August 2015 which they think was triggered by my first pregnancy).
Shehata specialises in recurrent miscarriage and looks at NK cells in the body (Natural Killer cells) which is a very common cause of miscarry and treatable by steroids.
He is definiately one to consider.
I also hear that Zita West (anothe private doctor) is an expert in recurrent miscarriage and specialises on the IVF side so also worth looking in to (it depends on your situation and type of complications you are having ie. not being able to conceive or not being able to carry?).
Anyway, whatever route you take I wish you all the best and I am happy to keep you posted about my journey with Shehata.
Lou x