"I still have my pen with me" is correct.
Still usually goes before the verb:
Do you still have a headache?
I still buy my milk from the supermarket.
She still swims every day.
I still haven't heard their last album.
However, there are exceptions:
I have still got the book you lent me.
I was still in bed when you called.
He is still at work.
We have still got to meet John.
Can anyone explain the rule regarding the placement of the word still? I'd try, but I'm not sure I'd get it right.