Sans-serif to go with EB Garamond (no math)?

If you don't mind an organic sans serif, you could use Linux Biolinum which is part of the libertine package; Libertine is a more modern (but still classical) typeface than Garamond, but the pairing still works rather well in my opinion (and if you want to pair a Garalde typeface with a sans serif, you probably don't care that much about period accuracy) -- although I wouldn't use bold sans (a double anachronism) for headers:

\documentclass{article}
\usepackage[sf,scale=0.95]{libertine} % sets biolinum as sf only 
\usepackage{ebgaramond}       
\begin{document}
\section*{\sffamily\mdseries Lorem Ipsum Redux}
Cras viverra metus rhoncus sem. \textsf{Nulla et lectus vestibulum} urna fringilla ultrices.
\end{document}

The current libertine package automatically uses otf by loading fontspec if the document is compiled using xelatex or lualatex, but the above works using pdflatex as well.

If you prefer a more classical sans serif, or really would like to use bold sans, you can try Pablo Impallari's Quattrocento Sans:

\usepackage[sf,scaled=0.9]{quattrocento}
...
\section*{\sffamily Lorem Ipsum Redux}

I think the typeface is okay for headings even in bold, but too wide to use in the text body.

Assuming the usage will be for headers or elements like folios, my choice would be Optima, which has a classical structure and so won't clash too much. If that's not to your liking, Syntax is a choice advocated on Typophile for this sort of thing, but its higher x-height would require some scaling down.

Another good choice could be Myriad or Frutiger. Myriad and Minion come with Adobe Reader, and work quite well together (see What best combination of fonts for Serif, Sans, and Mono do you recommend?). There are plenty of nice choices, though. If you don't need bold, Calluna Sans is free, as well as Fontin Sans.

EB Garamond With Myriad Pro

Minion and Myriad (bold)

Minion and Myriad (regular):