Some informations can be found in this thread:

Need help ... to use real USB Serial port

the directserial connection can be accessed with
"serial1=directserial realport:cu." listed in the config file, followed by the name of the connection, like "modem", so the full line will read:
"serial1=directserial realport:cu.modem", for example.

If it works for printers, I don't know. Printing at all is not supported by DOSBox, at is it not needed for games.

Thanks. I don't know if "modem" is the word to use since I don't know the word used by the system to describe the "port" that I print from to the network printer. That's the part I need help with specifically. I'll keep checking and read the thread.

That is the thread that I read initially but unfortunately in my case is specific to a USB printer. I think that "modem" in that case pointed to a USB port which I don't use to print out to the network printer.

Looks like port 515 is used to print to a network printer. Anyone know how I could specify that in a line of code for the config file? I'm pretty ignorant about this obviously. Thanks again.

First, tried:
serial1=cu.modem listenport:515 (when "tty" listed "cu.modem" which is currently "cu.Patti-1")

Didn't work.

ls /dev/tty.*

Shows
/dev/tty.Bluetooth-Modem
/dev/tty.Bluetooth-PDF-Sync
/dev/tty.Patti-1

I think "Patti-1" is the usb printer. That tty name wasn't listed until I defined the printer with a very simple name, using:
Name: LEX
Location: PWL
Queue Name: LEX
Host Name: localhost
Driver Version 1.0.3
URL: usb://Lexmark?Z600%20Series?serial=18K618523000610

I defined it that way because I read in another post that a simple name was important - don't recall just where I read it.

I edited the config file to:
serial1=directserial realport:tty.Patti-1
serial2=directserial realport:tty.Patti-1
serial3=directserial realport:tty.Patti-1
serial4=directserial realport:tty.Patti-1

When trying to print this way (to COM-1 or LPT-1) Console reports:
(among other things) is -
Jun 29 11:30:05 PWL DOSBox[222]: Warning once: This application, or a library it uses, is using NSQuickDrawView, which has been deprecated. Apps should cease use of QuickDraw and move to Quartz." - sounds suspicious to me!

no luck

Tried several other things, including the replacing "Patti-1" in the config with the serial number, "18K618..." still no luck.

This is a work project - I'm trying to get an old estimating program to print from a Mac. I've tried it under Parallels/Vista still no luck, even installed a printer driver on the Vista side, still nothing - get a check box as if the printing was successful but nothing printed 😀 however, I'd really rather not go the Parallels route. The boss wants to run a new 13-inch MacBookPro but the one old program he wants and needs to keep alive is this DOS program. All works except the printing. It's printing options are LPT-1, LPT-2, COM-1, COM-2.

if this 'Port 515' is a TCP port, you can try

serial1=nullmodem server:<ip of print server> transparent:1 port:515

Thank you! I disconnected the USB printer and connected the network printer (using a laptop next to my work, networked mac). Set the network printer as an IP printer rather than an appletalk printer, typed in the ip. Tried:
serial1=nullmodem server:128.129.112.243 transparent:1 port:515

no luck - console reported:
PWL kernel [0]: System Preference[286] Unable to clear quarantine '128.129.112.243.app': 93
... among other things.

Tried:
serial1=nullmodem server:ipp//128.129.112.243/ transparent:1 port:515
Console reported:
PWL kernel[0]: AppleYukon2 - en0 link down
PWL configd[14]: AppleTalk shutdown
PWL configd[14]: AppleTalk shutdown complete

If I wanted to use the USB printer, any idea if that would be simpler?
Thanks so much.

For ports < 1024 you need to run it with root access rights.

Now that's definitely over my head. I'm logged on with administrator's rights on the Mac. Do I log in somehow in DOS?

Quarantine seems to have something to do with the Mac not trusting DOSBox. But that's from Google, I don't know much about Macs.