Microsoft SQL Server can be run on macOS using Docker, allowing developers to create a cross-platform environment for .NET Core applications. To get started, download and install Docker for Mac, increase the default memory allocation, and then run the SQL Server container with specific parameters. The SQL CLI tool provides a convenient way to query databases, while Azure Data Studio offers an alternative to SQL Server Management Studio for managing and administering SQL Server instances. Developers can also use this setup on Windows or Linux platforms, making it a versatile option for cross-platform development with .NET Core.