I can think of a few ways, but they're kind of out there
and
won't work most of the time:
If the remote box is running SNMP and you know its community string
you can SNMP poll it to get its mac address
If the entire path from you to the remote host is IPv6 and not IPv4,
the boxes MAC address is part of its IPv6 address by default (this can easily
be overridden).
Why do you need the remote box's MAC address? If you're trying to use
MAC address to uniquely identify users or something like that MAC (or any type of network address)
is not the way to do it.