Rates on the route are up 57.1 per cent compared to 2020 and are up 162.2 per cent compared to 2019.
Prices from Shanghai to North America increased 20 per cent in the final week of the month due to Covid-crisis disruptions.
Shanghai to Europe rates jumped 30 per cent in the final week of August.
'This is no way close to the pace of rate changes given a baseload of medium to long-term contracts still fills up the Asia-Europe and Asia-US markets,' said Freight Investor Services head of air and containers Peter Stallion.
Prices from Hong Kong to Europe increased 1.1 per cent in July to $4.63 per kg.
Rates on the route are up 54.6 per cent compared to 2020 and up 80.8 per cent compared to the same month in 2019.
On services from Frankfurt to North America rate increases continued to slow after a spike at the end of 2020 and in the first few months of 2021.
Rates from Frankfurt to North America were down 3.9 per cent in July at $3.94 per kg and were two per cent down last year.
Said Stifle senior analyst Bruce Chan: 'The European Union recommendation [that its member states restrict non-essential travel from the US] will be implemented differently by different members, creating imbalances in capacity that follow passenger demand, and not freight needs,'
'And different policy restrictions, different terminal shutdowns, and sporadic infections are likely to make planning even more challenging.' said Mr Chan.