We present the characterization of a laser frequency stabilization scheme using a state-of-the-art wavelength meter based on solid Fizeau interferometers. For a frequency-doubled Ti-sapphire laser operated at 461 nm, an absolute Allan deviation below 10−9 with a standard deviation of 1 MHz over 10 h is achieved. Using this laser for cooling and trapping of strontium atoms, the wavemeter scheme provides excellent stability in single-channel operation. Multi-channel operation with a multimode fiber switch results in fluctuations of the atomic fluorescence correlated to residual frequency excursions of the laser. The wavemeter-based frequency stabilization scheme can be applied to a wide range of atoms and molecules for laser spectroscopy, cooling, and trapping.