@Kim mimi Where did you want to get Married?
For example In Germany and in italy you Can marry without withdrawing your asylum claims. In fact you shouldn't withdraw your asylum claim while trying to get Married in both countries. Asylum seekers can marry legally in both countries as far as you provides the legal documents for your marriage. Although it may not be as fast as you may expect. But you have to be patient and wait for thier replies.
In other to contract a legal marriage in Germany or in italy you will need this Documents
(1) Passport or National identity Card
(2) Birth certificate, showing place of birth names and other identity of your parents
(3) a single Status Certificate, Certificate of no impediment Also called the Bachelorhood Certificate in German (Ehefähigkeitszeugnis) in Italian (Nulla Osta) this Certificate state that you are free to Marry and that you aren't married and also that there aren't any obstacles in your ways of getting married.
But there's an exception to this for example if your country doesn't issue an Ehefähigkeitszeugnis. For Example countries like Nigerian, Pakistan, Iran and many more you can apply to the Regional high court for exception of the Ehefähigkeitszeugnis.
As some embassies aren't allowed to issue the Ehefähigkeitszeugnis in the name of Germany except Germany recognises your country as an Ehefähigkeitszeugnis issuing country. But if its in Italy you can contact your country of Origin Embassy and get the Nulla Osta there taking your fiancee, the person you wants to Marry Nulla osta (certificate of no impediment) you can get it the same day from the Embassy.
(4) if any of you were married in the past you need to present a Divorce degree Certificate showing that the Marriage have been totally dissolved.
(5) you also need to provide 2 witnesses if necessary an interpreter. You can also ask the Standesamt to provide them for you. If you can't get it yourself. But be prepared to pay a few more Euros
(6) the Civil Ceremony usually cost around 110-to 200 Euros, however there might be additional fees during your application process for having some special documents approved, getting married in a different state or a special venue.
(7) lastly keep in mind that the Marriage ceremony at the standesamt are always performed at the weekdays although some cities can make an exception for this if you are willing to pay more.
I hope this answered your questions if not you can post other questions in the Comunity for more experienced people to answer.