Removing the SIM Card from an Iridium 9505A: The first step is to remove the antenna and the battery. The SIM holder is underneath the battery. If you are looking at the SIM holder with the top of the phone pointed up, the SIM holder can be "gently" slid back and forth from the left to right. Use your thumb to "gently" slide the SIM holder to the left which is the "unlocked" position. Then simply use gravity to let the SIM holder swing out so that the SIM itself can be pulled out of the SIM holder.
Inserting the SIM Card: Putting in the new SIM is the reverse process. Put the SIM in the holder and "gently" push it flush so that the "gold contacts" point down. Then use your thumb to "gently" slide it to the right "locked" position. You should feel a subtle click. You are done.