Games like Port Royale 3
Games like Port Royale 3 include Port Royale 4, Manor Lords, Cities: Skylines, Railway Empire, and Jurassic World Evolution. We matched them by the tags players give Port Royale 3 on Steam (Strategy, Trading, Simulation, Pirates, and Economy): closest matches first, and among equally close ones the better-known games.

Port Royale 4
Shared: Strategy · Trading · Simulation

Manor Lords
Shared: Strategy · Simulation · Management

Cities: Skylines
Shared: Simulation · Strategy · Management

Railway Empire
Shared: Strategy · Simulation · Management

Jurassic World Evolution
Shared: Simulation · Strategy · Management

Victoria 3
Shared: Strategy · Simulation · Economy

Sid Meier's Pirates!
Shared: Pirates · Strategy · Naval

Transport Fever 2
Shared: Strategy · Simulation · Management

Workers & Resources: Soviet Republic
Shared: Strategy · Simulation · Management

Planet Coaster
Shared: Simulation · Strategy · Management

UBOAT
Shared: Simulation · Naval · Naval Combat

Europa Universalis V
Shared: Strategy · Simulation · Trading

Anno 1800
Shared: Strategy · Simulation · Economy

Supermarket Simulator
Shared: Simulation · Trading · Management

Jurassic World Evolution 2
Shared: Simulation · Strategy · Management

Cities: Skylines II
Shared: Simulation · Strategy · Management

Patrician III
Shared: Strategy · Trading · Simulation

Sailing Era
Shared: Strategy · Simulation · Management

Against the Storm
Shared: Strategy · Simulation · Management

Imperator: Rome
Shared: Strategy · Simulation · Management

Crusader Kings III
Shared: Strategy · Simulation · Management

Empires of the Undergrowth
Shared: Strategy · Simulation · Management

Corsair Cove
Shared: Strategy · Simulation · Management