Assuming it's a startup with high growth ambition with real potential, the most common thing to offer is equity from the company (or company to be registered later).
The amount of the equity you should offer depends on the stage at the startup development http://www.startupcommons.org/startup-key-stages.html
The earlier it is the higher is the risk of that equity to have any real value, as well as the time that it would materialize.
The other factor is naturally for how long and how much of time usage would you be expecting from the mentor, as well as how valuable you consider that mentoring to be on the success of the company.
The good thing about equity arrangement is that if both party see the value on doing this, also the reward to benefit from the relationship is aligned via equity arrangement.
Generally in startup mentoring, many serial entrepreneurs are quite happy to offer some general advise for free as part of their "giving back", this they will typically like to do as part of their own networking or presentations in a startup events. I would say that if they are in the event, they are available, so just be brave enough to ask.
However, beyond simple one off advises, if you feel you need to build a longer relationship, it's better to not expect the availability of the good mentors to have time available without some arrangement either directly or via some accelerator program or similar.
For short term need you can naturally always opt in for a simple cash transaction and even use same model over period of time "as needed" bases. Now clearly something like Clarity offers as easy as it can get solution for this. Optionally you could setup a simple "monthly fixed fee" as well.
In case it's for something else than startup that basically have these generic models available, then you may think of something similar, where you share some of the upside (what ever that is) with the mentor.
If it's totally something out of "traditional business" like life coaching, you could simple offer you own skills, contact network and time in return, assuming the would be a match in what the mentor (or his/her business, network etc.) would have use for. Something that is easy for you, but not so for the mentor.
Recommendations. I love offering my insight and mentoring folks and often all I ask is that wherever they end up my name goes with them. Referrals and recommendations are a huge value just knowing there are people other then myself out there spreading my name.
The mentoring relationship exists primarily because the mentor want to "give back". A good mentor will typically not be motivated by personal gain. (And if they are, they will likely not be a very good mentor).
I typically believe that success happens in business by providing an opportunity for gain, however I think this may be an exception.
A mentor may benefit from the contacts and potential business relationships that may be created by a successful protégé, however these are generally secondary and will not happen in the short term.