San Mateo County supervisors have ordered rent freezes for building owners. Landlords will not be able to increase rent through May 31, the end of the shelter in place order. This has been another step the county has taken to help tenants, they previously banned evictions for people who can't afford to pay because of loss of jobs due to COVID-19. Contra Costa County has also ordered rent freeze.
The Emergency Regulation took effect on April 28, 2020 and will remain in place until May 31, 2020, unless it is extended by the Board of Supervisors. The Emergency Regulation is Countywide, which means it applies in all cities located within the County as well as in the unincorporated areas.
Various cities like San Jose, Oakland, and Alameda have their own rent freeze measures. You can get more information for the emergency regulations here.