Baudenbacher served as a member of the Supreme Court of the Principality of Liechtenstein between 1994 and 1995. In 1995 he was appointed judge of the EFTA Court upon a proposal of the Principality of Liechtenstein. From 2003 to 2017, he served as the Court's President. The EFTA Court hears cases originating from the EFTA States which are Contracting Parties to the EEA Agreement (currently Iceland, Liechtenstein and Norway). The EEA Agreement has extended the EU single market to those EFTA States. It is based on a two pillar approach. Both pillars, the EU pillar and the EFTA pillar, have their own surveillance authority and their own court. EEA law which has been implemented into the legal orders of the EEA/EFTA States is capable of having direct effect and eventually takes precedence over conflicting national law. The EFTA Court has recognized EEA State liability. Moreover, EEA law must be interpreted in the light of fundamental rights. The EFTA Court is bound by homogeneity rules to follow or to take into account relevant ECJ case law. In the majority of its cases, it is, however, faced with novel legal questions and consequently has to ‘go first.’ There are countless references to EFTA Court case law by the ECJ, its Advocates General, the General Court and high courts in Germany, Austria, the United Kingdom, Sweden, and Switzerland. In practice, the one-sided written homogeneity rules have largely been superseded by a "unique judicial dialogue" (ECJ Advocate General Verica Trstenjak). Frequently described as a very influential member of the Court, Baudenbacher acted as the Reporting Judge in a number of landmark cases including E-16/16 Fosen-Linjen; E-3/16 Ski Taxi; E-5/16 Vigeland, E-29/15 Sorpa; E-14/15 Holship Norge AS v Norsk Transportarbeiderforbund; E-4/15 Icelandic Financial Services Association v ESA; E-27/13 Gunnarsson; E-25/13; Engilbertsson; E-15/12 Wahl; E-16/11 Icesave; E-14/11 DB Schenker; E-15/10 Posten Norge; E-9/11 Regulated Markets I; E-18/11 Irish Bank; E-14/10 Konkurrenten; E-1/10 Periscopus; E-1/06 Gaming Machines; E-3/06 Ladbrokes; E-4/04 Pedicel; E-1/04 Fokus Bank; E-2/03 Ásgeirsson; E-3/02 Paranova v Merck; E-3/00 Kelloggs; E-1/99 Finanger; E-1/98 Astra Norge; E-3/97 Opel Norge; E-2/97 Maglite.
