Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Add butter. Once butter is melted and hot, stir in rice. Cook, stirring occasionally, until rice becomes opaque, about 2 minutes. Stir in water, chicken broth, lime juice, and salt. Close and lock the lid.
Select high pressure according to manufacturer's instructions; set timer for 4 minutes. Allow 10 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer's instructions, about 5 minutes. Release remaining pressure carefully using the quick-release method, about 5 minutes more. Unlock and remove the lid. Stir in lime zest and fluff rice with a fork.
Serve immediately with lime wedges, garnishing with chopped cilantro.