Will web browsers cache content over https

By default web browsers should cache content over HTTPS the same as over HTTP, unless explicitly told otherwise via the HTTP Headers received.

This link is a good introduction to setting cache setting in HTTP headers.

is there anyway to tell them it's ok to cache?

This can be achieved by setting the max-age value in the Cache-Control header to a non-zero value, e.g.

Cache-Control: max-age=3600

will tell the browser that this page can be cached for 3600 seconds (1 hour)

As of 2010, all modern, current-ish browsers cache HTTPS content by default, unless explicitly told not to.

It is not required to set cache-control:public for this to happen.

Source: Chrome, IE, Firefox.