I understand the first part, being introspective and non judgemental.
however, I don't get the link between meditation and emotional intelligence.
Well, meditation is always helpful and teaches you how to focus on the present and on that one thing only, as well as accept what is as it comes and goes.
However, what I meant is that parts of my method are based on basic mindfulness practices. For example, body scan is a technique where instead of focusing only on breathing, you proceed to gradually scan your whole body - essentially you check in with each part to look for any tension, cold, tiredness etc. I use a similar approach to analyse each part of myself, literal and metaphorical, in an effort to find possible traces of what could be caused by an emotion - and through analysis of these traces I am able to learn how each emotion feels without further physical analysis. It takes a lot of visualisation at times, too, as well as confusion and flailing around.
In short, I compare the observed differences with my default equilibrium - the neutral, almost blank, state I find myself to be most often in.
But then, I found that there are at least two different neutral states in me - one that arises as a numb answer to too much input (uncomfortable neutral) and one that arises as an answer to calm (comfortable or peaceful neutral). I call the former one numbness and it's the most prevalent in my depressive episodes. The latter I call being content. In general I base emotions around temperature, from warm, through neutral, to cold, kind of like a spectrum

.
I'm sure that it'll be different for everyone since we're all completely different people.
I suppose it can be a bit difficult to get with words only, since for me it's highly based on feeling (kind of blindly) and visualisation. I would suggest trying things for yourself until you find what seems to work for you. Just don't get discouraged. It took me the better part of the last three years to even start on the road of discerning emotions and more subtle emotions still seem to elude me.
Still, there's progress!