Spin-lattice relaxation measurements with surface coils used in the single coil mode on stationary samples will produce accurate T1 values if a three-parameter exponential fit is employed. A further sufficient requirement is that the T1 measurement method (pulse sequence) conform to the following three criteria at all points in the sensitive volume of the surface coil. (i) The Z magnetization is consistently prepared to a nonequilibrium value at time zero. This initial condition must be the same at the start of every evolution period. (ii) After preparation, the magnetization is allowed to return toward thermal equilibrium during variable evolution periods τ. (iii) A constant fraction of the Z magnetization must then be sampled (observed) at the end of the evolution period. The inversion recovery, modified fast inversion recovery, and pulse-burst saturation recovery methods meet criteria (i)-(iii) and produce accurate T1 values with a surface coil. A brief survey of surface coil T1 measurements suggests that the greatest dynamic range is provided by using the inversion recovery or modified fast inversion recovery method, the pulse-burst saturation recovery method provides accurate T1 measurements in a minimum amount of time, and the use of composite pulses does not significantly improve the accuracy of the measurement.