I don't know of any prayers for such cases (other than ones regarding the lack of Temple services), there are many cases where one might be inclined to use something else instead (like using a lemon instead of an Esrog). In certain cases, it seems like it is better to 'fake it', so to speak, so as to do something even if it isn't the mitzvah, while in other cases this might be prohibited.
Let me elaborate. The Gemara specifically addresses the case of someone who lacks an Esrog:
אתרוג לא יביא לא רמון ולא פריש ולא דבר אחר, פשיטא, מהו
דתימא לייתי כי היכי שלא תשכח תורת אתרוג, קמ״ל זימנין דנפיק
חורבא מיניה דאתי למיסרך.
If someone couldn't find an Esrog, he should not take a pomegranite or quince or anything else in it's stead. [Is this not] obvious?! One might have thought [that such a thing should be done] in order so as not to forget the law of the Esrog, so [the Tosefta] comes to teach us that sometimes destruction could come through such an act, as someone might come to be drawn after it (Sukkah 31b)
While the Gemara gives no prayer or the like for such a situation, it appears that it's better to do nothing than to hold a lemon instead of an Esrog, because one might mistakenly come to think that taking a lemon is a fulfillment of something. The Rambam (Sukkah 7:5) extends this to the other 3 species as well.
There are important exceptions to this rule of "not faking it". After all, there were several enactments made in order so as not to forget certain laws that depended on the Temple, which includes not only prohibitions (such as the fact that new grain is prohibited for entire 'yom hanef') but also positive institutions, such as waving the four species every day of Sukkos, and in a different way, the entire institiution of eiruvei chatzeros (see Eiruvin 46b, 80b) and taking Challah from dough in areas that would otherwise not require it (see Bechoros 27a). In these examples, where there's no possibility of 'destruction' (since the worst that would happen is that people do extra things that they aren't supposed to do, not that the fake rituals would replace required commands) such actions were encouraged.
However, the differences between permitted 'mitzvah remembrances' and prohibited ones may not be so clear cut. The Gemara also brings (approvingly) the case in Menachos 32b of the 'Munbaz household', who placed their Mezuzos on sticks in a manner which was not a fulfillment of the mitzvah when it was a time of danger.
There is one further case where the Sages explicitly stated doing something for the mitzvah at a time when it can't be fulfilled in actu: regarding Channukah candles. In a case of 'a time of danger', when one cannot place the candles where they would be seen, the Gemara Shabbos 21b says to place them on the table. (However, this may either be, as Tosfos explain, because there's also a fulfillment of pirsumei nisa in the house, or because Chanukah candles don't actually have to be visible to others). A friend of mine used this as fodder for a nice piece of Channukah drush
This plays regarding another question as well. According to some opinions, (Shyarei Knesses Hagedolah O.C. 143:1, brought by the Magen Avraham there) if a congregations does not have a Sefer Torah than they should read the appropriate reading from a printed book specifically "so as not to forget about the law of Torah reading". Even though others prohibit this practice, it appears that they do so only out of respect for the congregation, and not because they are worried that someone might come to think that reading from a Chumash or invalid Torah scroll is enough (See Aruch Hashulchan 143:7). Perhaps the difference between this case and that of the Esrog is that here, (1) the Torah portion is actually being read (i.e. people are still learning Torah) so at least something is being accomplished (2) since Torah reading is something done in public, we aren't worried that people will come to mistakenly think that it doesn't need to be done with a Torah scroll. The way in which this dispute is recorded in the Shibbolei Haleket (Tefillah 31), however, it appears that Rashi was opposed to this practice precisely due to the misdirection produced by such a practice, though it could be that he was only so opposed because Berachos were made on these readings of invalid sifrei Torah