You can pick a Humanist Sans, for instance:
ITC Stone Humanist
ITC Officina Sans
FF Scala Sans
Jannon Sans

Thank you! I'll check those out.

This is a tricky proposition.
You might be better off using something like ITC Legacy Serif and Sans.

You may also try:
Rotis Sans Serif (featuring a small eye as in Garamond)
Parisine
FF Yoga Sans
FF Nexus Sans (featuring a small eye as in Garamond)

I've matched Adobe Garamond with Seria Sans, as well as (maybe less successfully) Myriad.

Maybe this:
http://typographica.org/typeface-reviews/beorcana/

hhp

May I suggest my own Proza? It was initially intended as a sans-serif companion to Garamond, and still shares its humanist skeleton. You can read all about it here: http://ilovetypography.com/2013/11/01/making-fonts-proza-typeface/

For similar proportions you might try this: http://www.myfonts.com/fonts/storm/jannon-sans/
It's based on Jannon, rather than Garamond, but it's probably the closest of a match you'll find.

Good luck!

Thanks to everyone for all the suggestions!