The Madeira weather during summer is very mild. The climate is very temperate. Temperatures range from a minimum in January of 13 C (55F) to 26 – 27 C (79F) in July, August and September.
For fishing, I suggest wearing a light jacket, shorts, and/or slacks, as it can get a bit cool, especially in the evening. Similar attire is suitable ashore, as long as it's presentable. It's also advisable to pack a jacket, shirt, and tie. Ladies may want to include some more formal attire. While you may not need them, certain places appreciate a touch of formality. However, it's unlikely to rain during the summer months.
Madeira has a typical Mediteranean climate* with winter rain in December, January and February. Bring a raincoat at this time.
This great climate is why the grapes do so well and the wine is so good!
Polaroid sunglasses or clipons are a must. With them you may see a Marlin behind the lures as well as the crew (that will take a while!).
If you're acquainted with the Mediterranean, you'll find that Madeira boasts better weather, although the café scene may not be as vibrant. Dress as you would for St. Tropez and revel in being the center of attention.