Recent proposals for open service GNSS signal authentication, including the GPS Chimera  protocol, rely on delayed release symmetric key cryptography. This allows the receiver to determine that a signal, or navigation message, was authentic, provided that the receiver has a reliable, secure, but loose, time synchronization prior to receiving the GNSS signal. The key requirement is that the receiver must be certain that the symmetric key has not already been released at the time that the authentication information is received. Recent work  has shown that secure time synchronization requires a two-way time transfer mechanism. In this work we investigate two candidate secure wireless time transfer protocols, namely Network Time Security (NTS) over Network Time Protocol (NTP) and Roughtime , to establish their suitability for use in providing the level of secure time synchronization required by the proposed GPS Chimera scheme. A series of experiments were conducted in both static and dynamic environments and the bounds on uncertainty in the time estimates provided by the two candidate schemes were evaluated. It is shown, that in all the tests conducted, a standard 4G wireless internet connection was sufficient to provide a secure time transfer capability with a bound of less than ±300 ms for both candidate protocols. This bound is well within the requirements of the Chimera scheme, suggesting that either Roughtime or NTP could be considered suitable candidates for providing secure time synchronization for use with Chimera.