There are many suggestions for dealing with this, and it's hard to nominate one as 'best', as they are all somewhat experimental at this stage. It also depends on the need of each site.
One method that's worth considering is a menu that collapses to a button on small screens, as demonstrated in this recent thread:
Of course, there are some much more sophisticated versions of this online.
What options have you found so far? Have you researched this at all yet?