You can based the stop on the underlying but when underlying hits your stop, you sell your option at bid, and buy at ask.
As an example, take GILD which I trade, one month out ATM call of $79 has a bid of $3.8 and ask of $5.8. So, if you are long and want out with a stop, you sell it at $3.8 if you are short and want out with a stop, you buy it back at $5.8. Manually we usually get our transaction done at mid.