In Sales, some customers ask for a quotation only to compare prices. How can we get business from them?

It is actually very true that many customers request for quotations to compare prices and also other potential customers do the same.

For the case of existing customers, your main obligation would be to turn them into loyal customers thus the strategies would mainly be centred at customer relationship management because they are already existing customers. Maintaining, enhancing, establishing long term relations with customers or formation of bonds between your business & your customers is a key issue in relation to customer relationship management while creating loyal customers. 

For the case of potential customers or prospects, your obligation would be to turn them into real customers & thereafter repeat customers thus the strategy would be regularly or frequently contacting or following up after issuing quotations to them. You can as well send them business proposals with attractive or eye-catching features to persuade them into choosing your product. 

Thanx for the invitation.

In order to get business or a sale for customers that request a price or query, especially if the price is beaten by competitors, you must provide a difference. By my experience, the easiest way to do this is to offer unbeatable customer service - if they feel you can serve them better than the competition by customer service and are more approachable, you will increase your chance of gaining their business.