Not an expert on
NMM in the slightest (I don't like it as a technique)....
But none the less just talking about how reflections work.
If you think about the reflection on a flat surface as your "baseline" case, then on a convex surface the reflection should be squished closer together, sharper, tighter, whatever terminology you want to use. If there's a bright reflection, that bright spot should get smaller.
The opposite is true of a concave surface to a point, the reflection will become larger, more stretched out.
The "to a point" is the literally until you reach the focal point of the curved concave surface, at which point the image flips and then it behaves more like a convex lens, just flipped. You only really need to think about that when the curve is very sharp meaning your virtual observer and the object being reflected would beyond the focal point.
As for how your sword looks, I think it looks good, though it doesn't really look terribly "metal" to me, from your specular source reflection (the extreme bright point) you want it to transition more rapidly into the diffuse reflection (the bright area which is darker than your specular reflection, but brighter than the dark area which isn't reflecting light).
If you don't have the rapid rise in contrast up to your specular source reflection and instead just have a consistent and smooth gradient across the whole surface, the specular reflection gets lost and you only get a diffuse reflection, which means the surface looks dull instead of shiny and it'll tend to look more like stone or maybe a sandblasted metal rather than a vibrant and shiny metal.
Another possible suggestion, push your specular light source reflections all the way to white, it'll assist in making it look like a reflective metal vs a flat/matte object.
Another thought, the backside of the blade near the hand, where there's a cutout and the blade is kicking back up towards the tip, you've painted that dark but in my mind there should be another bright spot, but perhaps that depends on the lighting. Also perhaps the hole and the ribs nearer the handle should also have some reflections/bright areas.
But yeah, I'm not a expert nor a great fan of
NMM because it makes my head explode too much at the complexity, though I enjoy thinking about the physics of it,
lol.
The couple of times I tried to paint
NMM, I actually painted it true metallic first (using something like VMC Dark Aluminium) to figure out where reflections would be under certain lighting conditions and then tried to mimic that with some modifications around edges which aren't sculpted to scale.
EDIT: I should add part of the reason I don't like
NMM is because I can't do it properly and I think 99% of the people who attempt it can't do it properly and would be better served doing true metallics,
lol, but here's a great example of
NMM done right and he walks through some of the thoughts and processes.
https://razzaminipainting.blogspot.com/2016/07/non-metallic-metals.html