I know that there are a few companies that rent bikes in Portugal, mostly scooters in popular tourist destinations, like the Algarve.
Here is a link with two companies:
Here is a list where some companies claim to rent motocycles, though the information might not be reliable. None of them list a website.
This company I know used to rent bikes, including BMW F650s, but their website doesn't display any information on that.
Renting vehicles in Portugal is generally
more expensive than in North America. A few years ago I looked into renting a bike and found the above site that rented F650s
for about $80 US/day. I found it to be too expensive for me, so I didn't bother to investigate further.
I used to live in Portugal. There are a lot of bikes on the road. On a single day in Lisbon I counted more than 20 BMW F650s and hundreds of other bikes.
Traffic is very different from North America. Bikes weave all the time through traffic, lots of speeders and people taking chances.
The accident rate is at least double what it is in North America.
Traffic aside, the country is beautiful. Despite the fact it's small, it has so much to see and experience. If you're in the Lisbon area, head out to Cascais and Cabo da Roca. The road has great twisties and the view is awesome. On Sundays you'll see a lot of bikers on the Cascais-Cabo da Roca road and the Cape (Cabo da Roca) is a meeting spot of sorts for bikers.