The issue is probably not what you think. It is probably that the mail server you are sending the mail through (either your company's mail server or your company's ISP's mail server) does not accept mail originating from outside its network. This is a pretty standard tactic for dealing with spam.

Two solutions present themselves. One is does the relevant mail server provide authenticated SMTP? If so, it should accept SMTP from outside the network. Earthlink, for example, is like this. You can only use SMTP if you are directly connected, but if you use authenticated SMTP you can connect from anywhere.
Alternatively, do you have access to a work machine that is on 24hrs a day? If so you can use ssh tunnels to handle this for you. This is a subject discussed at length in macosxhints so I'll just give the highlights:
(1) In your /etc/xinetd.d directory create a file called smtp_via_ssh and populate it with the following text
service smtp
{
disable = no
only_from = localhost
socket_type = stream
wait = no
user = usernameOnThePortable
server = /usr/bin/ssh
server_args = usernameOnTheWork24hrComputer@24HrComputerName.com -c blowfish -q nc localhost 25
groups = yes
}

(2) in Apple mail, set all mail to be delivered using localhost port 25.

(3) switch off postfix

(4) reboot