Yes, you can either emulate a COM port (fake modem) or you can have it pass through to the host system.

How do you get it to pass through the host system?

From dosbox.conf:

[directserial] # directserial -- Enable serial passthrough support. # comport -- COM Port inside DOSBox. # realport -- COM Port […]
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[directserial]
# directserial -- Enable serial passthrough support.
# comport -- COM Port inside DOSBox.
# realport -- COM Port on the Host.
# defaultbps -- Default BPS.
# parity -- Parity of the packets. This can be N, E or O.
# bytesize -- Size of each packet. This can be 5 or 8.
# stopbit -- The number of stopbits. This can be 1 or 2.

directserial=true
comport=1
realport=COM1
defaultbps=1200
parity=N
bytesize=8
stopbit=1

I did all of that and I still can't access the com port.

The support is limited. Direct physical access should work, but some BIOS(?) functions are not implemented yet. It was discussed here before (try to search).
CANADACOW said he would have a look on it (so *maybe* in a future version).
Anyway: what are precise errors in the program and/or DOSBOX?

Mirek

I have this old program that I use and it uses an external modem to dial out to other machines. When I try to run it in DOSBox it tells me that there is no com port. I have the modem attached to com 1 and dosbox setup with directserial on com one, but the program still can't seem to find the com port.