Why don't we have proton/neutron microscopes? According to wave-particle duality it should be possible for protons/neutrons to have wavelengths shorter than those of electrons having similar velocity. So why don't we use proton/neutron microscopes for probing into further detail.
 A: It seems that proton microscopes exist

Recently a new high energy proton microscopy facility PRIOR (Proton Microscope for FAIR) has been designed, constructed and successfully commissioned at GSI Helmholtzzentrum f\"ur Schwerionenforschung (Darmstadt, Germany). As a result of the experiments with 3.5-4.5 GeV proton beams delivered by the heavy ion synchrotron SIS-18 of GSI, 30 um spatial and 10 ns temporal resolutions of the proton microscope have been demostrated. A new pulsed power setup for studying properties of matter under extremes has been developed for the dynamic commissioning of the PRIOR facility. This paper describes the PRIOR setup as well as the results of the first static and dynamic proton radiography experiments performed at GSI. 

Neutrons being neutral are harder to control, but as the link RobJeffries gives in the comments shows, neutron microscopes have been demonstrated.

We have demonstrated a prototype neutron microscope, which uses magnification-4 Wolter mirrors, with samples and a detector aligned at the mirrors' two focal planes.

A: I don't know how pertinent is my answer, but actually they should have gone much farther, as FIBs (Focused Ion Beam) microscope use heavier atoms (usually Gallium).
However, I'm not sure that they achieve a better resolution than SEMs, because beyond a certain value of momentum the ions start to damage the sample.
A: We have neutrons microscope. The main difficulty is to get free neutrons. Those only exist as bound state with proton in atoms' nucleus. One need nuclear reaction to get them out ! Two possible choices : nuclear reactor with bored reactor vessel (politician love it) or spallation source (proton beam shot on a target producing nuclear fission and a bunch of free neutrons). Any of those solutions need big facilities and are definitely bigger than a electron microscope... : https://en.wikipedia.org/wiki/Neutron_research_facility.
Main purpose of those neutrons beams are neutron scattering : it probes samples without destroying them (or much less than X-ray) : https://en.wikipedia.org/wiki/Neutron_scattering. And you can get lot of information about the shape of your molecule or crystal composing the sample, the energy quantum state and so on. Very useful for condensed matter physics, chemistry and biology and medicine (also there is a bit of particle and nuclear physics in those facilities, neutron beta decay is very interesting, plenty of observable for testing the standard model and add constraints on the physics beyond the standard model)
