What is the most convenient way to get between Haneda and Narita. Once at Haneda, I would have a 4 hour layover before by flight from Narita to the U.S. How long will the transfer between the 2 airports take? Both flights would be on Nippon so would I have to claim by bags at Haneda and check them again at Narita? I haven't booked the flights yet just looking into possibilites. I am using FF miles and am flying from Osaka to Haneda. Thanks.

Most convenient by far is the limobus. Takes about 75-90 minutes to get from one to the other, costs 3100Y. Yes, you need to pick up your bags at Haneda and take them to Narita. The airline's name is ANA or All Nippon Airways.

Did you look for flights from Osaka Itami airport (ITM) to Narita?

4 hours is a very short time for this transfer. May not be impossible, but something I would not attempt.

Thanks for your replies. I am currently booked Itami to Narita but have the possibility of adding a couple extra days to our stay. Using FF miles two days later though only offers the option of Itami to Haneda. No biggie I just thought I might get a couple extra days. Thanks again.

You can take the train to Narita Airport. I suppose you are leaving from Kyoto. The fare would be about $140 minus the $10 you would pay to get to Itami. If you can combine that trip with other JR travel on a JR Pass then you might be able to save some of that cost.

Or you fly to Haneda the day before, but within 24 hours, of your departure from NRT. That might work.

http://www.webjet.com/travel/airport-transfers-tokyo/
Tokyo residents usually relied on trains. We know consistent traffic jams in this city. However, direct express trains are less frequent than limousine buses.
http://www.keisei.co.jp/keisei/tetud.../us/index.html

There should be a direct train first travelling on Keikyu tracks, then on the Asakusa metro line and finally on the Keisei line. Or simple transfers between these three operators could be arranged, if memory does not fail me, at Sengakuji and Oshiage.

Another possibility could be Keikyu train to Shinagawa station, then NEX to Narita. I suppose it should be faster as there are fewer stops.