www.thefreedictionary.com/warrantee

A warranty guarantee, including for the repair of guarantee defects, is a non-payment guarantee and an irrevocable obligation of the bank to pay a monetary amount up to a set amount in the event that the applicant does not meet its contractual obligations during a guarantee term and does not correct defects arising during the guarantee term.



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Note added at 3 hrs (2010-03-17 06:58:10 GMT)
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Benefits

The guarantee represents quality security for the obligation of a supplier (applicant), and the customer (guarantee's beneficiary) obtains certainty that it will receive performance from Raiffeisenbank under the guarantee in the event that the supplier does not perform its contractual obligations during the guarantee tenor and if the recipient (beneficiary) asks for performance in accordance with the conditions of the guarantee.
It strengthens the trustworthiness of the supplier (applicant) in relation to the customer (beneficiary).

If "Bürge" (i.e., the "Bürgschaftsgeber") is "guarantor," then it makes sense to simply call the "Bürgschaftsnehmer" the "guarantee."

Here is a dictionary entry for "guarantee" as the party, to whom a "guaranty" is made:

GUARANTEE, contracts. He lo [sic] whom a guaranty is made.
2. The guarantee is entitled to receive payment, in the first place, from the debtor, and, secondly, from the guarantor. He must be careful not to give time beyond that stipulated in the original agreement, to the debtor, without the consent of the guarantor; the guarantee should, at the instance of the guarantor, bring an action against the principal for the recovery of the debt. 2 Johns. Oh. R. 554; 17 Johns. R. 384; 8 Serg. & Rawle, 116; 10 Serg. & Rawle, 33; 2 Bro. C. C. 579, 582; 2 Ves. jr. 542. But the mere omission of the guarantee to sue the principal debtor will not, in general, discharge the guarantor. 8 Serg. & Rawle, 112; 3 Yeates, R. 157; 6 Binn. R. 292, 300.
See http://legal-dictionary.thefreedictionary.com/guarantee

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Note added at 7 hrs (2010-03-17 11:01:11 GMT)
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guarantee
[...]
3) n. occasionally, the person to whom the guarantee is made.
[...]
See http://dictionary.law.com/Default.aspx?selected=840

I don't have my Black's at hand (I'll check when I get into the office), but I am relatively certain that it contains the same definition for "guarantee."

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Note added at 8 hrs (2010-03-17 11:14:58 GMT)
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Additional (off-topic) Information

The following is admittedly blind citation, as I took it from a blog discussion at AdamsDrafting.com on the difference between "guarantee" and "guaranty" (which is obviously not directly related to your question, though interesting nonetheless), but this is what Bryan Gardner has to say in A Dictionary of Modern Legal Usage (1995):

The distinction in BrE once was that the former [guarantee] is the verb, the latter [guaranty] the noun. Yet guarantee is now commonly used as both n. & v.t. in both AmE and BrE. … .

In practice, guarantee, n., is the usual term, seen often, for example, in the context of consumer warranties or other assurances of quality or performance. Guaranty, in contrast, is now used primarily in financial and banking contexts in the sense “a promise to answer for the debt of another.” Guaranty is now rarely seen in nonlegal writing, whether in G.B. or in the U.S. Some legal writers prefer guaranty in all nominal senses.

Guaranty was formerly used as a verb but is now obsolete as a variant of guarantee, v.t.

See http://www.adamsdrafting.com/2006/10/05/guaranty-or-guarante...

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Note added at 11 hrs (2010-03-17 14:35:16 GMT)
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David's suggestion would work (it is the original creditor, to whom the guaranty is usually given) and is undoubtedly more common. But I think the tendency to give this party such a name is based on an assumption that "guarantee" is the promise itself (and it is, in fact, often used that way), and that it could be confusing for the reader. If one drafts the "guaranty" carefully, however, the meaning of the words should be clear:

"There are several uses of the word 'guarantee' in today's parlance, however the following should be used in legal documents. Guaranty is the actual document containing language of assurance. Guarantor is the entity giving the guaranty and guarantee is the entity receiving the guaranty. Following conventional English spelling rules, therefore, the plural of guaranty or verb usage of the word should be guaranties, [...]."
See http://en.wikipedia.org/wiki/Surety

Here is another reference for my take on this:

"LAW ON GUARANTEES.

1. A guarantee (also spelled guaranty) is a written promise
that a person will perform some duty or answer for the pay-
ment of some debt, in case of the failure of another person.

2. The person who guarantees the faithfulness of another is
called the guarantor.

3. The guarantee is the person to whom the pledge is made.

4. All guarantees must be in writing.

[...]"
See http://www.archive.org/stream/safebusinessmeth00nichrich/saf...

Surety contracts in the USA are issued by insurance companies. The beneficiaries of the insurance are called the "Insured." All of the other answers supplied so far are correct under American all. But they are general. Warrantees and guarantees may exist under any old type of contract. This is a surety agreement, so in my legal judgment, the warrantee, or the guarantee or the beneficiary of this deal is most clearly and specifically called: the "Insured."