Recommended!
ares is a multi-emulator, successor of higan, and is the latest promising newcomer of N64 emulation, started by Near, version 130 has added 64DD emulation and macOS support for Parallel-RDP. It tries to strive on accuracy, clean code and ease of use as much as possible. However it might require performant hardware because of its accuracy, but it's worth it!

Project64 is among the oldest and most compatible N64 emulators around that is still updated today. 64DD emulation was added since version 2.3, and has improved a lot since, and supports disk swapping!

A special Project64 build has been made for 64dd.org where it adds the following plugins: GLideN64 (up to date), angrylion-rdp-plus and parallel, the 64DD IPLs have been automatically setup so you can go straight to it, and easier N64 Mouse setup.

mupen64plus is one of the longest standing N64 emulators that can emulate 64DD, while not fully compatible at times.
You can use Rosalie's Mupen GUI with a nice brand new Project64 style interface and improved support for 64DD games, it includes every relevant plugins including parallel-rdp and rsp and a brand new easy to setup Input plugin.

M64Plus FZ is an adaptation of mupen64plus for Android devices. The Free version has some ads, while the paid Pro version removes them and includes online cloud backup and netplay support.
64DD support is a little limited, but playable depending on your device's performance.

RetroArch is a popular frontend that also can download tons of emulator cores.

MAME, the known multi system emulator, has been the very first emulator to support 64DD, coded by Happy_.
All the other emulators has used its 64DD emulation code as a base at one point.
Requires 64DD disk dumps to be converted with ddconvert. A tutorial is available for MAME, but I don't suggest to use it.

MiSTer FPGA is the open source FPGA project where you can play tons of consoles, handhelds and other systems in the standard FPGA board DE10-Nano. FPGA is a reprogrammable electronic chip, meaning compared to software emulation, this acts like an actual electronic chip that can simulate the systems using cores. A Nintendo 64 core was made recently which supports the fanmade 64DD cartridge ports ROM files, a large SDRAM extension board is required. Unfortunately, you cannot save in those 64DD games.