Imperfect measurement of uncertainty (deeper uncertainty) in climate sensitivity is introduced in a two-sectoral integrated assessment model (IAM) with endogenous growth, based on an extension of DICE. The household expresses ambiguity aversion and can use robust control via a 'shadow ambiguity premium' on social carbon cost to identify robust climate policy feedback rules that work well over a range such as the IPCC climate sensitivity range (IPCC, 2007a). Ambiguity aversion, in combination with linear damage, increases carbon cost in a similar way as a low pure rate of time preference. However, ambiguity aversion in combination with non-linear damage would also make policy more responsive to changes in climate data observations. Perfect ambiguity aversion results in an infinite expected shadow carbon cost and a zero carbon consumption path. Dynamic programming identifies an analytically tractable solution to the IAM.