What the law actually says
The threshold is 5 kW of engine power — a little under 7 horsepower. Below it you need no licence and no certificate of competence to take a boat out in Croatian waters. Above it you need a proper skipper's licence, and rental companies do check, because the harbourmaster fines them rather than you. Note that the limit is stated in kilowatts and advertised by some rental firms in horsepower, which is how people end up in a boat they are not entitled to drive.
What that gets you
A small open boat, four or five metres, doing perhaps six or seven knots flat out. That is enough to cross to Čiovo, work along the Marjan shore, or spend a day drifting between the coves on the south side of the peninsula with the anchor down. It is not enough to reach Brač comfortably, and it is emphatically not enough to be out in wind. Treat it as a floating picnic table with a motor and it is one of the best days you can buy here.
The coves on the south side of Marjan are the same ones in snorkelling the Marjan shore — bring a mask.
If you want someone else to drive, a skippered day sail will take you to Šolta or Brač.
What it costs and what to check
Roughly €57 a day in the shoulder months and €88 and up in high season, usually with fuel extra and a cash or card deposit held against damage. Before you leave the pontoon: confirm the engine is genuinely under 5 kW and get it in writing, check there are enough lifejackets for everyone including children, ask what the boat's insurance excess is, and get the operator's phone number. And look at the forecast — a small boat and the afternoon maestral are a bad combination, which is why the sensible plan is out early and back by two.
For how a boat day compares with everything else, see is Split expensive?
Things to do in Split
Boat trips and tours
Split in one day