great question, Naarkon's friend!

I am also fascinated in how people make custom-anything, and especially the maps.
I'm thinking Mapmaker etc would know the exact recipe.
Forgive my speculation here, what follows is I conjecture how it's made.

First, a highquality
600DPI+ 3D map is made in the image program of your choice.
This then has to be true CBYMK'd to be "print-ready".
this is important, as it can be an additional fee some printers will charge by the hour (or part therof)
to make un-CBYMK'd work into CBYMK'd print ready.

Next, these digital maps are printed at a local printers (say, officewerks etc),
on ~110gsm satin gloss A0 paper that's trimmed to size.
A SWMinis map is slightly larger than A3 size.
I think this necessitates a minimum order size and what not.

After this point, i do not know where the laminated maps originate -
perhaps they are laminated at the local printers etc,
or by hand.

In Japan, it may be possible to have a map the exact size of a SWMinis map printed 1:1, as it is close to B2.
there would be a 1-3mm white border around the edge, which could be trimmed.

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the above is how you would make a custom map that looks and feels like an 'official' SWMinis map,
for in-home and rapidprototyping/playtesting you could as easily use
an A1/A0 printer and print, or for a slightly smaller map,
an A3 printer,
if it's lazerjet, it comes out looking pretty awesome.
You can then scotchguard or laminate as you see fit, to ensure no moisture damages.
If you wanted to try making tiles for tile-wars,
I recommend strongly, checking your printer's guidebook to see if your printer will accept 180GSM cardstock PRIOR to attempting to print hehehe (I learned that one the hard way doh)

Now, as to cost,
I cannot provide a precise guesstimate*,
though a lot depends on run-size, ink used per job etc,
if you supply your own materials etc...
it can be somewhat expensive, as a lot of places do not do a once-off run
for just 1 map (even though they could,
there's no tooling etc, they just make an excuse to print more hehe)
I would be keen to learn more about this step in the process,

Thanks for asking a great question, Naarkon,
I hope this gives a little extra perspective,
and I hope you get a more definitive answer from those-in-the-know soonish.
hopefully it shouldn't be too long
before we see your custom maps on the customs thread hehe