We report on a continuous-wave alexandrite (Cr3+:BeAl2O4) microchip lasers operating at 680.4 nm and 749.5 nm laser wavelengths. Microchip resonators were realized by dielectric mirrors directly deposited on the alexandrite crystal surfaces. InGaN laser diode providing up to 3.5 W of the output power at ∼445 nm wavelength was used as a pump source. More than 210 mW and 570 mW of the laser radiation have been extracted from the microchip laser systems at 680.4 nm and 749.5 nm wavelengths, respectively. The corresponding slope efficiencies related to absorbed pump power were 15 % and 39 %.