Departure: Funchal. Several companies offer boat excursions from Funchal port.
Best time: From April to September.
We went on an excursion with Magic Dolphin in late March. We chose a very sunny, windless day. We were lucky to see several dozen dolphins in the bay in front of Funchal: alone, in large groups, in trios with babies. It was an incredible experience! The guide told us it was the best day for dolphin watching since the beginning of the year. However, we didn't see any whales. It is not allowed to touch or swim with the dolphins. Some companies offer reduced rates in case of an excursion day without dolphin sightings for you to have the experience again.
In conclusion, this experience is a must if you're staying in Madeira for a week and the weather conditions are ideal. You'll spend a half-day on a boat to perfect your tan, with a view of Funchal Bay and possibly the first cliffs towards Cabo Girao (depending on the location of marine mammal groups) and dolphin/whale watching! In the afternoon, we took the opportunity to visit Funchal the market, the botanical/tropical garden, and enjoy a great restaurant: link.