Unfortunately you have to manually check and debug this issue as there is not much in UI for debugging these types of issues.

Have you tried turning on the Debug setting in the shipping settings ?

That will log your API requests into your var/log/ directory.

Also if still you don't have idea about what causing issue then you can manually check for following things:

The function that handles shipping rules and values in checkout process is

Mage_Shipping_Model_Shipping::collectCarrierRates().

You could check whether it is being called at all or not, it should be called atleast once in your checkout process.

You could try debugging this core function by putting Mage::log() so that you could get idea which line causing issue.

Refer below link for more details:

Debugging: Sorry, no quotes are available for this order at this time

Unfortunately you have to manually check and debug this issue as there is not much in UI for debugging these types of issues.

Have you tried turning on the Debug setting in the shipping settings ?

That will log your API requests into your var/log/ directory.

Also if still you don't have idea about what causing issue then you can manually check for following things:

The function that handles shipping rules and values in checkout process is

Mage_Shipping_Model_Shipping::collectCarrierRates().

You could check whether it is being called at all or not, it should be called atleast once in your checkout process.

You could try debugging this core function by putting Mage::log() so that you could get idea which line causing issue.

Refer below link for more details:

Debugging: Sorry, no quotes are available for this order at this time