I think that this is actually pretty subjective. I know that plenty of people would say Alejandro Paul’s scripts are contemporary because they’re some of the best and most popular new script faces being used in contemporary work. But other people would point out that Alejandro and his collaborators are excellent historians in addition to being excellent type designers, and that his work is partly revivals of script by the masters of the past.

Then there are the very popular grunge scripts by designers like Eduardo Recife, with overlapping ornaments, double lines, etc. distressed, and auto-traced. Sure some of them are just rehashes of older designs, but others are new, unconventional, and absolutely gorgeous. But the argument can be made that grunge design of any sort is the echoes of postmodernism’s death rattle, and that the nostalgic scripts that get more use are still more contemporary.

And it might be that technology is what defines a contemporary script, that style is irrelevant, and what really makes them contemporary is having a giant Opentype table full of CALT subs that allow it to make up for the tiny number of people who can still use a pen or brush to write legibly. But if we go there all the people who don’t like the idea of technological determinism will start to bitch…

Anyway, I’m going to stop before I get really pretentious, but I think you see what I mean about it being subjective.

Tools, and their implications.
I can hardly imagine a monoline script produced with a felt-tip pin look authentically old – or dated, respectively – no matter how flourished you make it.

Duffy Script is a contemporary script font.
It is based on the lettering of a contemporary illustrator, and utilizes state-of the art OpenType technology for pseudo-randomization of 4-variants-per-glyph, offering multiple permutations of any text.

You can try this effect of contextual alternates here.

@James Eduardo Recife does some really cool type faces.

When I was reading about Burgues it said that it was '[an] ode to the late 19th century American calligrapher Louis Madarasz' and that got me thinking about how contemporary it is. But I have seen other scripts such as for this cloths company All Saints that I consider to have quite an old skool look but still contemporary - so I know where you are coming from when you say it is subjective.

@Florian Yeah and anything like this: My Fonts

@Nick Interesting the use of the pseudo-randomization. It does look contemporary. It doesn't do much for me though.

It is based on the lettering of a contemporary illustrator…

That’s definitely a better way of defining contemporary than my babbling!

I pointed this out before, but using the word "contemporary" is useful only for describing prevailing trends of the moment, but by the time it is described the moment is already past, and no longer contemporary.
One runs into the same problem with "modern".

@cuttlefish what would you suggest as a preferred term?