Most of the tugs and barges monitor channel 13
Radio channels: There are actually 5 different organizations that regulate the use of marine radios. They have recognized three radio channels for safety purposes:
Channel 16: Distress, safety and calling
Channel 13: Intership navigation (bridge to bridge)
Channel 70: Digital Selective Calling (DSC)
1. In general everywhere in the world some regulatory agency has mandated that everything that floats with a VHF radio continuously monitor channel 16 when not actively using the radio. Yes, most big ships monitor multiple channels but they all monitor channel 16! By international convention 16 is the channel to use to call them.
2. The procedure after
making initial contact is to shift to another channel to talk. There are "commercial channels" and "recreational channels." See U.S. VHF Channels
Most ships will ask you to shift to a "commercial channel." Being very anally retentive it used to bother me since I was not a commercial vessel. Then I realized they weren't recreational vessels. I learned to go with the flow.
3. Frequently ships will pick either channel 6 or 10. I speculate this is because lots of people monitor 13. By using 6 or 10 they don't wake up the watch standers on all the other ships (lol.)
4. Frequently you will hear recreational boats suggesting you go "up one" - in other words to channel 17 from 16. Please note that it is illegal for a recreational boater in the United States to transmit on channel 17 unless talking to a state or local government entity. Channel 17 is a common ship to ship channel in international waters. If asked to go "up one" I suggest that you suggest a different channel - e.g. 68.
The US Coast Guard as a nice web page at Radio Information For Boaters
with lots of marine radio information.
Fair winds and following seas.