as already said - scan or take a picture of the page with your picture/info and email it to yourself (and also save it on your computer)....
also, print that copy out and put it with your travel documents (like you set sail pass, etc)....
but as for the passport itself, keep it with you in your purse when you travel...
i have my passport in a leather holder that's the size of my passport, but that just goes right into my purse...
(actually, that leather holder holds both my passports, since i have dual citizenship and must use both passports when i travel)..
anyway, when i travel with the family, i have a whole lot of passports in my purse (doubling up for almost everyone), but it's got to be in the bag that you never put down...and that's my purse...
the moment you no longer need the passport (often right after you hand over your boarding pass), take a moment to put your passport into your purse....do not pass go, do not collect $200.
I always put it back into my purse each time i have to take it out..
in other words, after going through security, i stop, put it back into my purse and only then walk to the gate...if i need it again at the gate, i pull it out and then put it right back after handing over the boarding pass. I get it back into my purse as soon as possible.....without delay...