I've never ridden pillion very much but recently had an excellent 
experience passengering with Dave Edmondson at pilot while in London. 

I found that it upset the bike much less if I rode with the pilot, that
is, if I looked over his shoulder and anticipated when I should hold on
hard for braking or acceleration. I tried to always look over the
inside shoulder on corners and move as little as possible, leaving
Dave to manage me and the bike as he normally would the bike and 
luggage.

Hard acceleration can be quite unnerving as the feeling of being spit 
off the back is hard to fight. Similarly, I held on to the grab handles
tightly when Dave needed to brake so as not to mash him to a pulp (I'm
a lot bigger than he is...). Reaching around him and pushing off the 
tank seemed like it would be very awkward and make it even harder for 
him to manage.

On the rare occasions when I carry a passenger myself, I absolutely
refuse to carry anyone who is not properly accoutered for riding. That's
helmet, jacket, gloves, stout pants and shoes/boots as a minimum. It's 
not my responsibility to provide this gear, but it's my responsibility
to require it if they want to ride.

And I agree with an earlier poster: if you've not had much experience
carrying a particular passenger and especially if you've not carried
many passengers before, take a few gentler rides of some duration before
you head off to a difficult road like Mines/Mt. Hamilton. That's a 
nasty place to find yourself in trouble.