Insulin administration during insulin-modified intravenous glucose tolerance test (IM-IVGTT) can induce transient hypoglycemia in healthy insulin-sensitive subjects. This triggers counterregulatory responses (CRR), which influence the kinetics of glucose and non-esterified fatty acids (NEFA) and undermines the accuracy of mathematical modeling methods that do not explicitly account for CRR. The aim of this study is to evaluate mathematical models of glucose and NEFA kinetics against experimental data in presence or absence of CRR. Thirteen healthy non-diabetic subjects underwent a standard IM-IVGTT and a modified test (GC-IM-IVGTT) with a variable glucose infusion preventing hypoglycemia. While model predictions fit very well glucose and NEFA data from GC-IM-IVGTT, they lagged behind observations from IM-IVGTT during recovery from hypoglycemia, independently of insulinemia, which did not differ significantly between protocols. A modification to the glucose minimal model, using glucose concentration below a threshold as signal for CRR, improves model predictions for both glucose and NEFA. The associated increase in endogenous glucose production correlates, among various CRR hormones, mainly with the dynamics of glucagon concentration. The modified minimal models introduce new parameters that quantify strength and duration of CRR following hypoglycemia. Although CRR represents an unwanted side effect in IM-IVGTT occurring only in insulin-sensitive subjects, this study provides new insights leading to improved procedures for estimating insulin sensitivity from IM-IVGTT, which may also allow for assessing the individual capacity of recovery from hypoglycemic events in patients treated with insulin or insulin-releasing drugs.