I present in this dissertation two topics of monetary policy making under model parameter uncertainty. The first topic is an assessment of the Brainardfs principle in monetary policy making in a new context. Brainard (1967) proposes that policy making under model uncertainty should be cautious in the sense that the policy maker would move his instrument less aggressively than in the absence of uncertainty. I assess this proposal in Chapter 2 by considering monetary policy in a New Keynesian economy with the cost channel developed by Ravenna and Walsh (2006). Uncertainty in the model comes from a coefficient that governs the direct effect of interest rate and output gap on inflation in the Phillips curve. The loss function is endogenous to the structural parameters. My results show that the interest rate response to a shock under model uncertainty is not necessarily stronger than that in the absence of model uncertainty. These results imply that the Brainardfs principle does not apply in this framework. The second topic is on the optimal delegation of monetary policy under parameter uncertainty. In Chapter 3, I model an economy in which there is policy planner who faces uncertainty about the slope of the Phillips curve and a central banker who believes he knows the economy with certainty. The policy planner makes use of a delegation method similar to the one initiated by Woodford (1999) to induce his central banker to implement his min-max commitment policy. The policy planner then solves for the parameters of the delegated loss criterion by matching his min-max optimal policy, in term of a targeting rule, with that of the discretionary policy conducted by his central banker. Delegation under parameter uncertainty requires choosing a central banker with a preference for an output gap stabilization weight of less than one. In this delegation framework, the robust policy can save up to an additional loss equivalent to a permanent increase in inflation of 0.06 percentage point from its target, compared to the non]robust policy. In addition, the robust delegation is found to dominate standard discretionary policy.