Italian ferry company Emilia Romagna Lines run services from Rimini (and nearby ports) to a handful of locations in Croatia - Rovinj (in Istria), the island of Mali Losinj and Zadar in North Dalmatia.

These routes are all operated with fast catamarans, so flying to Rimini would be suitable if you want to make a quick trip across the Adriatic; however, services depart Italy early in the morning, so you'd most likely have to stay the night in Italy - which of course is no bad thing!

Cesenatico/Rimini - Mali Losinj by Ferry
As mentioned, Emilia Romagna Lines run a catamaran service (journey time: 4 hours 25 minutes) from Rimini to Mali Losinj. (Journey time is 5 hours 15 minutes from Cesenatico.) The service also stops at Pesaro along the way.

As the route starts in Cesenatico, you might like to consider flying to Bologna Forli airport as an alternative to Rimini, as this airport is about 35km from the port.

Cesenatico/Ravenna - Rovinj by Ferry
The same company also runs a service from Ravenna (north of Rimini) to Rovinj in Istria. Journey time is 2 hours 45 minutes.

Bologna Forli airport is in fact a closer airport to Ravenna than Rimini, so it is advisable to fly here from the UK if you wish to utilise this ferry route.

The ferry route also starts in the port of Cesenatico (journey time to Rovinj: 4 hours) as mentioned above.

Alternatives to Rimini
We would suggest that it is probably better to fly to Venice or Trieste airports rather than Rimini if you wish to go to Istria or Kvarner, or to Ancona airport if you want to reach Dalmatia. Bus routes from Venice or Trieste and ferry routes from Ancona are more frequent (and year-round), so will provide you with more chances of reaching Croatia.

Flights from the UK to Rimini
Ryanair have flights from London Stansted, Bristol, East Midlands and Liverpool

Flights from the UK to Bologna Forli
Ryanair have flights from London Stansted, Edinburgh and Dublin

Useful Travel Links
Rimini Airport Information from the wonderfully named "Federico Fellini International Airport"
Bologna Forli Airport Information on getting to/from the airport
Trenitalia Train timetables for journeys within Italy