If the medical monitoring company does not provide a lock box you can purchase lock box at a home improvement store like this one:
I am replacing my front door lock with a Kwikset electronic combination lock. Schlage also makes an electronic combination door lock. Another choice is the Gate House electronic combination door lock at Lowes. It costs $69.95 and stores up to ten codes. It uses Kwikset key blanks if you need additional emergency access keys.
Regardless of what device you use you can give the access code to the key safe or electronic door lock to the emergency medical monitoring company and have them add instructions to open the lock box or electronic lock to the customer profile.