Basically, you can monitor the network ports for faults or test each link/path for errors.
- error counters on managed switch ports
- error counters on host/NIC side
- port status (link state, speed, duplex mode)
- device availability (ping, status page, telnet, ...)
SNMP can be used for permanent monitoring and generating automated traps in case of an error.
- have the deployed cabling (re)certified to the specs
- (extended) throughput test with gigabit link in both directions simultaneously (for all pairs), e.g. with iperf3
- check error counters afterwards
COM servers can have quirks of their own. Make sure you've got a decent device, the latest firmware installed and the power is reliable (PoE from the switch is best).
If you can't use continuous monitoring (client network/remote network without facilities) it's practically impossible to know if the network is (currently) working correctly. Note that finding and eliminating intermittent problems in a complex network is a science of its own.
Especially when the connection is running across the Internet there may be no way to ensure reliable operation, and the devices and protocols in question would need to be able to handle packet loss and buffer even lengthy outages. If that is not possible either you can't use a simple COM server and will need to use local buffering on a larger device, an embedded server or so.