grammar - Choice of さしあげる in お電話さしあげる

I'm a bit confused by the usage of さしあげる in this sentence from Kanji in Context:

ただ今、来客中ですので、後ほどこちらからお電話さしあげます。 We have a guest at the moment, so we'll call you later.

To me, お電話いたします or even お電話いたしてさしあげます are more grammatical. Maybe it's really お電話(を)さしあげます? (I'll give you a call).

Answer

[差]{さ}し[上]{あ}げる is [謙譲語]{けんじょうご} for words like あげる and やる, as well as してあげる. By itself it means to give (with a sense of great respect), and as a subsidiary verb ([補]{ほ}[助]{じょ}[動]{どう}[詞]{し}), it adds a great sense of respect (for the person receiving the action) to the verb it is helping.

[致]{いた}す is basically 謙譲語 for する.

電話（を）する（いたす） can be thought of as: "to call".

電話（を）してあげる（さしあげる） can be thought of as: "to give a call".

In the sentence, the callee is telling the caller to expect a call back. This creates a sense of "waiting"; so, instead of just "calling", the person will "give a call back" (i.e., 電話をしてあげる). However, in business situations 謙譲語 is preferred on the phone. So, the frank-sounding してあげる becomes 差し上げる.

As to お電話（を）いたしてさしあげます, converting back from 謙譲語 would yield 電話（を）してしてあげる, which is blatantly incorrect.