A host computer running a TCP connection transfers the connection to a TCP offload network interface device (NID) which performs certain network processes, thereby reducing the load on the host CPU. The NID later transfers the connection back to the host. The host and the NID maintain separate timestamp clocks which provide timestamp values for connections using the TCP Timestamp option. Synchronization of the host and NID timestamp clocks can be realized by transfer of a clock value. The NID or host receives the transferred TCP connection and the transferred clock value, and decides whether to update its own clock to equal the transferred clock value, the decision being guided by the requirement to never allow the timestamp clock to run backward. Acceleration of the timestamp clocks is prevented so that RTT measurements are accurate. Synchronization of the host and NID timestamp clocks improves performance and reduces erroneous connection drops.