How to get a Ships-of-the-Line?

Solution 1:

All the countries other than the Spanish can spawn a ship of the line.

These conditions under which SOLs can spawn:

• Ships of the line are only spawned by non-Spanish nations; in fact, the Spanish will never spawn any Frigate class ships.
• Ships of the line are only spawned when any non-Spanish places a bounty on the player of what appears to be no less than 30,000 gold pieces.
• Like all other New Warship -classified ships, Ships of the Line are spawned along trade routes that have been recently terrorized by pirates, enemy nations, or the player. For example, attacking merchant ships traveling from City A to City B will eventually spawn a New Warship traveling from City A to City B, though there is no guarantee of the New Warship being a Ship of the line.
• Ships of the Line will only spawn from Wealthy cities. City population also seems to be a deciding factor, as well as national prowess, ie a stronger nation is more likely to send out multiple Ships of the Line. The game, however, provides no hard data on this; ergo, there is no way to accurately confirm this theory.
• Ships of the Line seem to be the most frequent in 1680, uncommon in 1660, and rare in 1640. There are, as of yet, no confirmed sightings of any Ships of the Line in 1620 and 1600. It is unknown whether Ships of the Line can actually spawn in those eras. Ships of the Line do not behave like Pirate Hunter -class ships: they are simply sent out from one city to another, will display no preemptive hostility towards you, and must be attacked first.

I have had most success causing ship of the lines to spawn by finding a wealthy city and camping outside of it, attacking any trading ships that pass by.

Solution 2:

It seems that maybe you answered your own question in a guide I found.

Ship of the Lines are spawned from 1 of 3 ways.

1: A Hurt city that had over 600 troops has now less than 150

2: A New warship possibility after you have taken 50 ships of that nation (spain not included)

3.) Pirate Hunter if you have taken over 100 of that nation's ships and are near a city that is at least prosperous.

When fighting the ship you should have: Grapeshot Chainshot Copper plating Brass cannon Fine Grain Powder and Iron Scantlings

When fighting always use a zig-zag approach to get near to the SotL for grapeshot and also not to have your tail whipped.

Once captured Hurry to a city immediately so pirate hunter can't catch you or sink your prize.

These tips should immobilize the ship and is yours for the taking.

This was found on hookedonpirates.com and was made by someone with the same username as you. It might be the same people but I've tested this and it seems to work.

The only thing that I haven't been able to concur with is a Pirate Hunter Ship of the Line.