Vonage Holdings Corp. is delivering conflicting messages on its ability to deploy a substitute technology should the Internet phone provider lose its bid to overturn a jury’s verdict that it infringed on Verizon Communications Inc.’s patents.

Depending on the audience, Vonage has been alternately reassuring and bleak: Customers and investors are told a technological workaround is feasible to prevent a disruption in phone service. But in court, Vonage declares doubt about that same possibility as it seeks permission to keep using the disputed technology during the appeal.