There are (inexpensive < $10) passport pouches, which you can wear hanging from your neck--easily concealed if you wear a sweater (or under your regular shirt); some have multiple compartments for holding (1)airline tickets, (2)train passes etc. Most come with a Velcro flap to protect the contents of the pouch.
For the last 10 years, I had been using an even cheaper version, but when the strap broke, I decided to "splurge" and buy the $8.99 one I am using now.