Reading the video RAM directly to generate an HDMI signal gives you about the same image an emulator does. Loses a bit of the 'fuzzy retro' appeal imo ;)

The same approach is also used by the 'ZX HD' expansion for the ZX Spectrum which uses a Raspberry Pi for HDMI output instead of an FPGA and doesn't require soldering since the Spectrum has an expansion connector which can be used to read the video RAM.