Surface nuclear magnetic resonance (NMR) is a noninvasive geophysical method that is primarily used in hydrological investigations of shallow aquifers. An important parameter in surface-NMR experiments is the relaxation time T1. Information on pore structure and even hydraulic permeability/conductivity may be inferred from accurate estimates of this parameter. Estimates of T1 are usually obtained by evaluating the spin response of groundwater molecules to excitation by two sequential electromagnetic pulses, the second of which is delayed and phase-shifted by π relative to the first. We have discovered that variations of the excitation field with distance from the transmitter and common imperfections in the transmitted pulses introduce considerable bias in estimates of T1 (e.g., errors as large as 50%). We assess the significance of these problems via numerical simulations based on the Bloch equation. As a result of this assessment, we propose a novel yet simple modification to the T1 acquisition method that resolves the identified problems. Our new scheme involves applying two types of double-pulse sequence, one in which the second pulse is phase-shifted by π relative to the first (i.e., the current procedure) and one in which the second pulse is in phase with the first. Subtracting the voltage responses measured after each of the two double-pulse experiments eliminates the bias, thus allowing T1 to be reliably estimated under general surface-NMR conditions.