cd ~/.wine/dosdevices/
ln -s /dev/ttyS0 com1
ln -s /dev/lp0 lpt1

Source

Since Wine 2.8, serial and parallel ports are detected automatically when Wine starts. Windows serial ports follow a naming convention of the word COM followed by a number, such as COM1, COM2, etc. Similarly, parallel ports use LPT followed by a number, such as LPT1. Linux, Mac, and BSD each have their own device naming conventions, but in every case the serial or parallel device is located somewhere in /dev. You can see the mapping of Windows devices to Unix devices by looking in ~/.wine/dosdevices. For example:

$ ls -l ~/.wine/dosdevices/
total 0
lrwxrwxrwx 1 alex alex 10 May 13 21:21 c: -> ../drive_c
lrwxrwxrwx 1 alex alex 10 May 14 14:43 com1 -> /dev/ttyS0
lrwxrwxrwx 1 alex alex 10 May 14 14:43 com2 -> /dev/ttyS1
lrwxrwxrwx 1 alex alex 10 May 14 14:43 com3 -> /dev/ttyS2
lrwxrwxrwx 1 alex alex 10 May 14 14:43 com4 -> /dev/ttyS3
lrwxrwxrwx 1 alex alex 12 May 14 14:43 com5 -> /dev/ttyUSB0
lrwxrwxrwx 1 alex alex  8 May 13 21:22 d:: -> /dev/sr0
lrwxrwxrwx 1 alex alex  8 May 14 14:43 lpt1 -> /dev/lp0
lrwxrwxrwx 1 alex alex  1 May 13 21:21 z: -> /

Make sure you have the needed rights to access your computer's serial and parallel ports. On Linux, a user must typically be a member of the sys or dialout group to access serial ports, or the lp group to access parallel ports.

To override Wine's default device mapping, run wine regedit and create string entries in HKEY_LOCAL_MACHINE\Software\Wine\Ports where the entry name is the Windows device name and the entry value is the path to the Unix device. Continuing with the above example, to make COM1 the first USB-attached serial port, create an entry with the name COM1 and the value /dev/ttyUSB0. You might also want to create an entry named COM5 with no value to remove the COM5 device which is now a duplicate of COM1. After editing the registry, shut down Wine with wineserver -k and the next time Wine runs a program, your changes will take effect.

If you use a version of Wine prior to 2.8, you'll likely have to create symbolic links in ~/.wine/dosdevices yourself. For example, to make COM1 the first USB-attached serial port, run ln -s /dev/ttyUSB0 ~/.wine/dosdevices/com1.