FAR 61.3(a)(1) requires pilots to have their pilot certificate in their possession or readily accessible in the aircraft, and FAR 61.3(c)(1) requires the same for an appropriate medical certificate should one be required. If either of your certificates has been misplaced or destroyed, then you will need to make a request for a replacement per FAR 61.29.
For your pilot certificate, you may go to the Airmen On-Line Services to order a replacement pilot certificate. You will need to pay the fee which is currently $2.00. To replace your medical certificate, you may send your request as shown in FAR 61.29(b)(1) or call the FAA duplicate certificate desk at 405-954-4821, option 3.
Because both the replacement pilot certificate and medical certificate take time to be physically delivered to you, you may request a document conveying the temporary authority to exercise certificate privileges while on the Airmen On-Line Services site. This temporary authorization will be good for 60 days and can be emailed or faxed to you. You must carry this temporarily certificate in place of the original, but only up to 60 days or until you receive your permanent replacements, whichever comes first.
Further guidance on requesting replacements for pilot certificates and medical certificates is available online.
Please note, FAR 61.3(a)(2) also requires that pilots fly with a valid photo identification. If your valid photo identification has also been lost or destroyed, you will need to check with the appropriate issuing entity for replacement procedures.
