We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes and finitely-many maturities. The dual formulation converts this problem into a continuous-time martingale optimal transportation problem which we solve explicitly for Lookback options with nondecreasing payoff function. In particular, our methodology recovers the extensions of the Azéma-Yor solution of the Skorohod embedding problem obtained by Hobson and Klimmek (under slightly different conditions), those derived by Brown, Hobson and Rogers, and those obtained by Madan and Yor.