In case anyone missed the announcement: bitcoinj 0.15, with support for native segregated witness, has recently been released.
https://groups.google.com/d/msg/bitcoinj-announce/X6Zv1NSFxOk/KJACzHZMAQAJ
For operability testing, I just released new versions 7.0 of Bitcoin Wallet. For now, they still create a keychain of legacy addresses but they can send to native segwit addresses via Bech32.
Testnet: https://play.google.com/store/apps/details?id=de.schildbach.wallet_test
Mainnet: https://play.google.com/store/apps/details?id=de.schildbach.wallet (At the time of this writing, you need to opt into beta in order to receive 7.x: https://play.google.com/apps/testing/de.schildbach.wallet)
Receiving to native segwit addresses and spending from them will follow in the coming days and weeks.