How would this work with the .h and .m files? Do you have to convert code piece by piece?

First, of course, you can paste contents of both .h and .m files into our code block converter.
Swiftify automatically joins interface and implementation section for classes and other declarations.

Second, you can use our File & Project conversion where you can upload multiple (zipped) .h or .m files and get them joint and converted to .swift files.

Third, you can use our Finder extension (included in Swiftify for Xcode) to conveniently convert multiple files, folders, and even projects right from your Mac!

Finally, the Advanced Project Converter (included in Swiftify for Xcode and available in the Advanced plan) is the most convenient way for gradually converting your project to Swift.