Women's Business Centers Improvements Act of 2019 This bill reauthorizes the Women's Business Center Program through FY2023, raises the cap on individual center grants, establishes an accreditation program for grant recipients, and revises the duties of the Office of Women's Business Ownership. Specifically, the bill modifies the Women's Business Center Program to enable the Small Business Administration (SBA) to provide initial and continuation grants to eligible entities to operate women's business centers for the benefit of women-owned small businesses. An entity must agree to obtain matching, non-federal funds, and the SBA must (1) ensure an applicant has sufficient resources to provide the services for which the grant is being made, and (2) conduct an annual compliance review. The SBA must also publish standards for a program to accredit entities that receive grants from the Women's Business Center Program, and such entities' receipt of continuation grants shall be contingent upon their obtaining accreditation.