Beorcana
http://beorcana.com/
http://typographica.org/typeface-reviews/beorcana/

thanks, but I am trying to find something that feels a little bit more contemporary.

Not quite contemporary with Optima, a bit earlier, actually, but with a similar mid-century vibe:
http://www.identifont.com/show?8HA
http://en.wikipedia.org/wiki/Lydian_(typeface)
http://en.wikipedia.org/wiki/Albertus_(typeface)

I would suggest you look at Hypatia Sans Pro from Adobe, designed in the last few years by Thomas Phinney and issued in 2007.

https://www.adobe.com/type/browser/landing/hypatia/pdfs/Hypatia_Sans_lan...

Optima's far more interesting sister:
http://www.myfonts.com/fonts/neufville/pascal-nd/

hhp

Candara is about the same vintage as Beorcana. It's a Microsoft house-brand font, but I find myself using it in places where in the past I used Optima.

How about Ocean Sans?
http://www.identifont.com/similar?3Q7

Perhaps: http://www.fontspring.com/fonts/aviation-partners/beaulieu
Or edgier: http://www.myfonts.com/fonts/fontbureau/amira/

Or perhaps Proza: http://www.myfonts.com/fonts/bureau-roffa/proza/

Check this list

Accent Graphic

Magma is perhaps not that recent, but to paraphrase Tina Turner, "What's recent got to do with it?"

http://www.stonetypefoundry.com/magmaoverview.html

I think a lot of the above don’t fit the brief of “feeling contemporary.”

Here are a couple of less “old style” feeling fonts, that still have the flares of Optima:
Chianti http://www.myfonts.com/fonts/bitstream/chianti/
FF Legato http://www.myfonts.com/fonts/fontfont/ff-legato/

I would suggest Brown, but it is more grotesque than humanist. http://www.myfonts.com/fonts/shinn/brown/

...and I will concur that my own Hypatia Sans would be a reasonable choice here:
http://www.myfonts.com/fonts/adobe/hypatia-sans-pro/

Cronos Pro?

That's a nice and underrated option.

Which naturally leads to suggesting:
http://www.myfonts.com/fonts/ef/today-sans/
:->

hhp

I think you are straying into alternatives to Gill rather than Optima territory with Today Sans Hrant.

I think you are straying into alternatives to Gill rather than Optima territory with Today Sans Hrant.

It's really attractive thinks.

Clipping Path

I never thought typophile would attract spam.

Thanks for all your replies.

A nice, more calligraphic alternative to Optima is Publica by Karl-Heinz Lange, revived as PTL Publicala:
http://primetype.com/faces_info.php?fid=45