Harnessing Effective and Appropriate Long-Term Health for Moms On Medicaid Act of 2021 or the HEALTH for MOM Act of 2021 This bill allows state Medicaid programs to cover services that are provided by maternity health homes (designated providers or health teams that provide pregnancy and postpartum coordinated care services). Participating maternity health homes must meet standards set by the Centers for Medicare & Medicaid Services (CMS), including the ability to coordinate prompt access to services, develop individualized care plans, provide supportive services, and coordinate with pediatric care providers. States must conduct outreach to providers, pregnant women, and other relevant stakeholders on the availability of such health homes and must report specified information relating to the implementation and outcomes of such services. The CMS must award grants to states to develop plans for implementation. The bill also temporarily increases the Federal Medical Assistance Percentage (i.e., federal matching rate) for maternity health home services.