Later this year, the PlayStation Portable Remaster Series will become available (at least in Japan), offering HD versions of PSP games for your PS3. The games will come with a ton of extra content, but trophy support won't be among them.
While HD visuals, 3D compatibility, controller support and cross-platform saves will be included, the addition of trophies for the games won't. Why? Sony Japan isn't saying, but Siliconera speculates convincingly that it may be related to the fact you can transfer saves from the PS3 to the PSP, leaving them vulnerable to hacking. Nobody cares if a singleplayer save is hacked, but tinkering to get free trophies would not please Sony, nor those who work had to earn them.