You can easily take your passport to a notary public and have it copied and the copy notarized.
Then keep your passport in the safe and use the notarized copy when you have to present a passport for medications or to verify a credit card .
A notarized copy is accepted just like an original document and it can be folded up in your pocket or handbag. It doesn't cost much at the notary either.
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Another thing I do when going on a long trip is scan passport, tickets, credit cards (front and back) and take photos of all baggage and handbags, print them all out and carry them with me in a safe place, as well as emailing the scans to myself. Also important is to keep the phone number of where you have to call to cancel a lost or stolen credit card.
Once I had a bag which didn't arrive with me on my plane and it did help that I could provide a colour photograph of the missing piece to the baggage reclaim on my arrival at destination.