Will web browsers cache content over https

Question

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.

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)